Abstract
The present survey is formed primarily on the basis of works reviewed in the Referativnyi Zhurnal “Matematika” during 1976–1983 and is a continuation of surveys of the same name published in 1966, 1971, 1976 in the series “Albegra, Topologiya, Geometriya” (INT). Principal attention is devoted to finite simple groups and their classification.
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Literature cited
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P. P. Baryshovets, “On finite groups with complementable non-metacyclic subgroups,” Ukr. Mat. Zh.,31, No. 1, 6–12 (1978).
P. P. Baryshovets, “Non-Abelian groups with complementable non-Abelian subgroups,” Ukr. Mat. Zh.,32, No. 1, 99–101 (1980).
P. P. Baryshovets, “Finite non-Abelian p-groups with complementable non-Abelian subgroups,” Ukr. Mat. Zh.,32, No. 6, 798–802 (1980).
P. P. Baryshovets, “Finite nonsolvable groups in which subgroups of nonprimary index are nilpotent or are Schmidt groups,” Ukr. Mat. Zh.,33, No. 1, 47–50 (1981).
P. P. Baryshovets, “Finite nonnilpotent groups in which all non-Abelian subgroups are complementable,” Ukr. Mat. Zh.,33, No. 2, 147–153 (1981).
P. P. Baryshovets, “On a class of finite groups with complementable non-Abelian subgroups,” Ukr. Mat. Zh.,33, No. 3, 291–297 (1981).
P. M. Beletskii, “On groups of automorphisms of finite two-step nilpotent groups of prime period,” Usp. Mat. Nauk,35, No. 6, 153–154 (1980).
P. M. Beletskii and E. Morgado, “On a group of automorphisms of a finite Abelian p-group,” Ukr. Mat. Zh.,33, No. 5, 589–596 (1981).
V. A. Belonogov, “Normal complements and conjugacy of involutions in a finite group,” Algebra Logika,15, No. 1, 22–38 (1976).
V. A. Belonogov, “On a reducible representation of a p-group over a finite field,” in: Investigations in Modern Algebra [in Russian], Sverdlovsk (1981), pp. 3–12.
V. A. Belonogov and A. N. Fomin, Matrix Representations in the Theory of Finite Groups [in Russian], Nauka, Moscow (1976).
Ya. G. Berkovich, “Automorphisms of semidirect products with a characteristic commutative kernel,” Izv. Sev.-Kavkaz. Nauch. Tsentra Vyssh. Shkoly. Estest. Nauk, No. 2, 5–7 (1978).
Ya. G. Berkovich, “Finite p-groups containing fewer than pP cyclic subgroups of order p2,” Questions of Group Theory and Homological Algebra, Yaroslavl', No. 2, 69–73 (1979).
Ya. G. Berkovich, “Subgroups of symmetric and alternating groups,” Izv. Sev.-Kavkaz. Nauch. Tsentra Vyssh. Shkoly. Estesty. Nauk, No. 1, 5–9 (1981).
Ya. G. Berkovich, “Finite p-groups containing fewer than pP cyclic subgroups of order pn, n>1,” in: Mathematical Analysis and Its Applications [in Russian], Rostov (1981), pp. 10–16.
Ya. G. Berkovich, “A generalization of a theorem of F. Hall and J. Thompson on Hall subgroups of a symmetric group,” Questions of Group Theory and Homological Algebra, Yaroslavl' (1981), pp. 79–92.
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Yu. V. Bodnarchuk and V. I. Sushchanskii, “Calculation in a Sylow 2-subgroup of a symmetric group of degree 2n,” in: Calculations in Algebra and Combinatorics. Application in Algebra and Combinatorial-Theoretic Investigations [in Russian], Kiev (1978), pp. 87–101.
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A. V. Borovik, “A 3-local characterization of the Held group,” Algebra Logika,19, No. 4, 387–404 (1980).
A. V. Borovik, “On normalizers of 2-subgroups in finite groups,” Sib. Mat. Zh.,22, No. 4, 62–78 (1981).
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E. G. Bryukhanova, “The 2-length and 2-period of a finite solvable group,” Algebra Logika,18, No. 1, 9–31 (1979).
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E. G. Bryukhanova, “On groups of automorphisms of 2-automorphic 2-groups,” Algebra Logika,20, No. 1, 5–21 (1981).
A. S. Bulgak, “The Möbius function of the lattice of subgroups of a finite group,” Tr. Mosk. Inst. Inzh. Zh.-D. Transp., No. 653, 103–109 (1981).
A. I. Burtsev, “Groups with arithmetic conditions for classes of conjugate elements,” Preprint, Rybin. Avits. Tekhnol. Inst., Rybinsk (1982).
A. I. Burtsev, “Finite groups with conjugate p-elements of the same order,” Preprint, Rybin. Aviats. Tekhnol. Inst. Rybinsk (1983).
A. I. Burtsev, “Finite groups with conditions on classes of conjugate elements,” Questions of Group Theory and Homological Algebra [in Russian], Yaroslavl' (1982), pp. 139–140.
V. M. Busarkin, “Finite groups with Abelian centralizers of elements of odd order,” Algebra Logika,16, No. 4, 381–388 (1977).
V. M. Busarkin and B. K. Durakov, “A criterion for nonsimplicity of finite groups,” Sib. Mat. Zh.,16, No. 4, 684–690 (1975).
V. N. Busarkin and V. R. Maier, “Finite groups with nilpotent centralizers of elements of odd order,” in: 6th All-Union Sympos. on Group Theory, Kiev (1980), pp. 168–179.
Yu. P. Vasil'ev, “An algorithm for constructing on a computer automorphisms and solutions of questions of the isomorphism of finite groups,” Kibernetika, No. 5, 151–152 (1978).
Yu. P. Vasil'ev, “Description of finite nonsimple groups by means of a computer. IV,” Kibernetika, No. 6, 17–20 (1981).
Yu. P. Vasil'ev and A. K. Zherlov, “Description of finite nonsimple groups by means of a computer. III,” Kibernetika, No. 5, 145–146 (1976).
A. V. Vasil'eva, “On centralizer lattices of finite simple groups,” Sib. Mat. Zh.,18, No. 2, 263–273 (1977).
A. V. Vasil'eva, “Characterization of the group PSL3 by the centralizer lattice,” Algebra Logika,15, No. 5, 509–534 (1976).
V. A. Vedernikov, “On finite factorizable groups,” V All-Union Algebra Conf. Texts of Reports, Part 1, Krasnoyarsk (1979), p. 34.
V. A. Vedernikov and N. G. Duka, “On theorems of Schmidt, Chunikhin, and Ito,” in: Subgroup Structure of Finite Groups. Proc. Gomel'sk. Seminar, Minsk (1981), pp. 16–23.
V. A. Vedernikov, V. S. Monakhov, and L. A. Shemetkov, “On the connectivity of the graph of intersections of subgroups of a finite simple group,” Dokl. Akad. Nauk Bel. SSR,21, No. 5, 398–401 (1977).
B. M. Veretennikov, “On finite groups with an involution whose centralizer has a factor-group isomorphic to L2(2n),” Algebra Logika (Novosibirsk),21, No. 4, 402–409 (1982).
B. M. Veretennikov, “Finite groups in which elements of odd order do not centralize subgroups of order 8,” Preprint, Ural. Politekhn. Inst., Sverdlovsk (1983).
V. M. Veretennikov and A. A. Makhnev, “On finite groups with a restricted centralizer of an involution,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 10, 8–14 (1982).
A. L. Vishnevetskii, “Groups of class 2 and exponent p with commutant of order p2,” Dokl. Akad. Nauk UkrSSR, A, No. 9, 9–11 (1980).
XIV All-Union Algebra Conference. Novosibirsk, September, 1977, Part 1, Groups. Algebraic Systems. Texts of Reports. Inst. Mat. SO AN SSSR, Novosibirsk (1977).
XV All-Union Algebra Conference. Krasnoyarsk, 3–6 July, 1979. Texts of Reports. Part 1. Groups, Krasnoyarsk Univ., Krasnoyarsk (1979).
XVI All-Union Algebra Conference. Leningrad, 22–25 Sept., 1981. Texts of Reports. LOMI AN SSSR, Leningrad, Parts 1 and 2, 1981.
XVII All-Union Algebra Conference. Minsk, 14–17 Sept., 1983. Texts of Reports, Inst. Mat. AN BSSR, Minsk, Parts 1 and 2, 1983.
V All-Union Symposium on Group Theory. Krasnodar, 1–3 Oct., 1976. Texts of Reports (Inst. Mat. Sib. Otd. AN SSSR, Kuban. Univ.), Novosibirsk (1976).
VI All-Union Symposium on Group Theory. Cherkassy, 19–21 Sept., 1978. Texts of Reports, Kiev. Naukova Dumka (1978).
VII All-Union Symposium on Group Theory. Shushenskoe, 9–12 Sept., 1980. Texts of Reports. Krasnoyarsk Univ., Krasnoyarsk (1980).
VI All-Union Symposium on Group Theory. Sb. Nauch. Tre., Inst. Mat. AN UkrSSR, Kiev: Naukova Dumka, 1980.
VIII All-Union Symposium on Group Theory. Sumy, 25–27 May, 1982, Texts of Reports, Inst. Mat. AN UkrSSR, Kiev (1982).
Calculations in Algebra and Number Theory [Russian translation], Mir, Moscow (1976).
A. G. Ganyushkin, “Enumeration of the subgroups of a finite Abelian group (algorithm),” in: Calculations in Algebra and Combinatorics. Application in Algebra and Combinatorial Theoretic Investigations, Kiev (1978), pp. 123–136.
A. G. Ganyushkin, “Enumeration of the subgroups of a finite Abelian group (theory),” in: Calculations in Algebra and Combinatorics. Application in Algebra and Combinatorial Theoretic Investigations [in Russian], Kiev (1978), pp. 148–164.
A. G. Ganyushkin, “Semidirect and fibered products of groups,” Dokl. Akad. Nauk SSSR,266, No. 6, 1291–1294 (1982).
N. D. Gogin, “The Mathieu groups M11 and M12 and projective planes of order 9,” in: Problems of Algebra and Functional Analysis [in Russian], Petrozavodsk (1978), pp. 3–5.
M. I. Golovanov, “Subnormal Abelian subgroups of finite p-groups,” in: Investigations in Group Theory [in Russian], Krasnoyarsk (1975), pp. 15–23.
T. D. Gormash, “On the existence of normal subgroups in finite groups,” Dokl. Akad. Nauk BSSR,23, No. 5, 399–401 (1979).
T. D. Gormash, “On the normal structure of finite groups,” Dokl. Akad. Nauk BSSR,24, No. 11, 978–979 (1980).
T. D. Gormash, “On the solvability and p-solvability of finite groups,” in: Subgroup Structure of Finite Groups, Tr. Gomel'sk. Sem., Minsk (1981), pp. 23–29.
G. A. Davtyan, “On a class of finite p-groups,” Uch. Zap. Erevan. Univ. Estestv. Nauk,1 (134), 10–15 (1977).
O. V. Damova, “On the lattice of maximal subgroups of a finite group,” Sib. Mat. Zh.,23, No. 6, 74–79 (1982).
Yu. V. Dmitruk and V. I. Sushchanskii, “The structure of Sylow 2-subgroups of alternating groups and normalizers of Sylow subgroups in symmetric and alternating groups,” Ukr. Mat. Zh.,33, No. 3, 304–312 (1981).
I. P. Doktorov, “On finite groups with complementable normalizers of Sylow subgroups,” Mat. Zametki,14, No. 2, 149–159 (1978).
I. P. Doktorov, “On finite ABA-groups with nilpotent subgroups A and B,” in: Subgroup Structure of Finite Groups. Tr. Gomel'sk. Seminara, Minsk (1981), pp. 29–34.
I. P. Doktorov and L. F. Kosvintsev, “Finite SP-factorizable groups,” Uch. Zap. Perm. Univ., No. 343, 46–47 (1975).
N. G. Duka, “Finite groups the maximal chains of subgroups of which contain p-subnormal subgroups,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 9, 2–10 (1979).
B. K. Durakov, “Finite groups with given centralizers of elements of order 3. I-II,” Preprint, Redkol. “Sib. Mat. Zh.,” Sib. Otd. Akad. Nauk SSSR, Novosibirsk (1975).
B. K. Durakov, “Characterization of some simple finite groups by centralizers of elements of order 3,” Mat. Sb.,109, No. 4, 533–554 (1979).
F. D'apiash, “One criterion of p-nilpotence of finite groups,” Ann, Univ. Sci. Budapest. Sec. Math.,20, 99–106 (1977).
G. G. Dyadchenko, U. M. Pachev, and V. N. Shokuev, “On an identity in the theory of p-groups,” in: Structural Properties of Algebraic Systems [in Russian], Nal'chik (1981), pp. 31–34.
A. K. Zherlov and V. I. Mart'yanov, “Automation of the proof of theorems of group theory,” in: Algorithmic Questions of Algebraic Systems and Computation [in Russian], Irkutsk (1979), pp. 36–64.
E. M. Zhmud'. “On the structure of finite groups with uniquely generated normal divisors,” Questions of Group Theory and Homological Algebra, No. 1, 59–71 (1977).
N. A. Zhuromskaya, “A generator of finite groups with cyclic Sylow subgroups,” in: Subgroup Structure of Finite Groups. Tr. Gomel'sk. Seminara, Minsk (1981), pp. 34–38.
A. Kh. Zhurtov and V. N. Shokuev, “On coverings of finite sets,” Algebra Teor. Chisel, No. 2, 78–81 (1977).
D. I. Zaitsev, “Factorizations of polycyclic groups,” Mat. Zametki,29, No. 4, 481–490 (1981).
D. I. Zaitsev, “Ito's theorem and products of groups,” Mat. Zametki,33, No. 6, 807–818 (1983).
A. E. Zalesskii, “Linear groups,” Usp. Mat. Nauk,36, No. 5, 57–107 (1981).
A. E. Zalesskii, “Linear groups,” J. Sov. Math.,31, No. 3 (1985).
E. D. Zaplatina, “On finite groups with restrictions on the indices of subgroups in their normalizers,” in: Investigations in Modern Algebra. Sverdlovsk (1981), pp. 35–37.
V. I. Zenkov, “Finite groups with a small number of classes of iso-order nonmodular subgroups,” in: Investigations in Modern Algebra. Sverdlovsk (1977), pp. 43–55.
V. I. Zenkov, “On 2-Sylow intersections in finite groups,” in: Investigations in Modern Algebra. Sverdlovsk (1979), pp. 48–53.
V. I. Zenkov, “On intersections of Sylow 2-subgroups in centralizers of involutions,” Preprint, Ural'sk. Univ. Sverdlovsk (1980).
V. I. Zenkov, “On central intersections of Sylow 2-subgroups in finite groups,” Preprint, Ural'sk. Univ., Sverdlovsk (1979).
V. I. Zenkov, “Finite groups with a given centralizer of a central involution,” Algebra Logika,19, No. 5, 566–581 (1980).
V. I. Zenkov, “Intersections of Sylow 2-subgroups in finite groups,” in: Investigations in Modern Algebra. Sverdlovsk (1981), pp. 38–47.
A. A. Ivanov, M. Kh. Klin, and I. A. Faradzhev, “Primitive representations of non-Abelian simple groups of order less than 106,” Preprint, VNII Sistem. Issled., Moscow (1982).
N. F. Ivakhori, “Centralizers of involutions in finite Chevalley groups,” in: Seminar on Algebraic Groups [Russian translation], Mir, Moscow (1973), pp. 263–287.
A. P. Il'inykh, “Characterization of the simple O'Nan-Sims groups by the centralizer of an element of order three,” Mat. Zametki,24, No. 4, 487–497 (1978).
A. P. Il'inykh, “Construction of some finite groups,” in: Investigation of Algebraic Systems on the Basis of Properties of Their Subsystems. Sverdlovsk (1980), pp. 68–75.
A. P. Il'inykh, “Finite groups with a standard component of type,” Algebra Logika,21, No. 2, 162–169 (1982).
V. V. Kabanov, “Finite groups with large intersections of Sylow 2-subgroups,” Sib. Mat. Zh.,17, No. 5, 1188–1189 (1976).
V. V. Kabanov, “On intersections of Sylow 2-subgroups in finite groups,” Mat. Zametki,24, No. 5, 615–619 (1978).
V. V. Kabanov, “The intersection of Sylow 2-subgroups in finite groups,” in: 6th All-Union Symposium on Group Theory, Kiev (1980), pp. 60–68.
V. V. Kabanov and A. S. Kondrat'ev, “Sylow 2-subgroups of finite groups,” Preprint, Sverdlovsk, Inst. Mat. Mekh. Ural'sk. Nauch. Tsentr AN SSSR (1979).
V. V. Kabanov, A. A. Makhnev, and A. I. Starostin, “Finite groups with normal intersections of Sylow 2-subgroups,” Algebra Logika,15, No. 6, 655–659 (1976).
L. S. Kazarin, “On some criteria of nonsimplicity and solvability of finite factorizable groups,” Questions of Group Theory and Homological Algebra, No. 1, 72–93 (1977).
L. S. Kazarin, “On the product of two groups close to nilpotent groups,” Mat. Sb.,110, No. 1, 51–65 (1979).
L. S. Kazarin, “Criteria of nonsimplicity of factorizable groups,” Izv. AN SSSR, Ser. Mat.,44, No. 2, 288–308 (1980).
L. S. Kazarin, “On groups with a factorization,” Dokl. AN SSSR,256, No. 1, 26–29 (1981).
L. S. Kazarin, “On groups with isolated classes of conjugate elements,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 7, 40–45 (1981).
L. S. Kazarin, “Groups with a factorization,” Preprint, Yaroslav. Univ. (1981).
L. S. Kazarin, “On the product of an Abelian group and a group with a nontrivial center,” Preprint, Redkol. “Sib. Mat. Zh.” SO AN SSSR, Novosibirsk (1981).
L. S. Kazarin, “Automorphisms, factorizations, and theorems of Sylow type,” Mat. Sb.,120, No. 2, 190–199 (1983).
L. S. Kazarin, “On the product of finite groups,” Dokl. AN SSSR,269, No. 3, 528–531 (1983).
L. S. Kazarin, “Theorems of Sylow type for finite groups,” in: Structural Properties of Algebraic Systems [in Russian], Nal'chik (1981), pp. 42–52.
L. S. Kazarin and Yu. A. Korzyukov, “Finite solvable groups with supersolvable maximal subgroups,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 5, 22–27 (1980).
L. S. Kazarin and P. I. Trofimov, “Investigation of criteria for the existence of solvable normal subgroups and criteria of solvability for finite groups with a factorization,” Questions of Group Theory and Homological Algebra [in Russian], Yaroslavl', No. 2, 90–101 (1979).
L. A. Kaluzhnin, “On groups of automorphisms of finite p-groups,” Inst. Mat. AN Ukr. SSR, Preprint, No. 23, 3–5 (1980).
L. A. Kaluzhnin, V. I. Sushchanskii, and V. A. Ustimenko, “Application of the computer in the theory of permutation groups and its applications,” Kibernetika, No. 6, 83–94 (1982).
P. J. Cameron, “Finite permutation groups and finite simple groups,” Usp. Mat. Nauk,38, No. 3, 135–157 (1983).
N. K. Kasabov, “Reflection generated by the symmetric group,” Godishn. Vissh. Uchebni Zaved. Prilozhen. Mat., 1974,10, No. 3, 55–59 (1975).
K. Sh. Kemkhadze, “Finite groups satisfying a normalizer condition for nonprimary non-Abelian subgroups,” in: Group-Theoretic Investigations [in Russian], Kiev (1978), pp. 138–153.
A. P. Kovalenko, “Characterization of groups of Janko-Ree type and of the Hall-Janko group,” Algebra Logika,15, No. 3, 292–299 (1976).
A. P. Kovalenko, “On ranks of intersections of centralizers of involutions in finite groups,” Sib. Mat. Zh.,18, No. 4, 821–829 (1977).
A. P. Kovalenko, “On groups with a given centralizer of an involution,” Preprint, Krasnoyar. Politekh. Inst., Krasnoyarsk (1983).
G. S. M. Coxeter and W. O. J. Moser, Generating Elements and Defining Relations of Discrete Groups [Russian translation], Nauka, Moscow (1980).
E. A. Komissarchik, “Simple groups with a number of conjugacy classes less than thirteen,” Dokl. AN SSSR,237, No. 6, 1269–1272 (1977).
E. A. Komissarchik, “Organization of a program on a computer for enumerating simple groups with a small number of classes of conjugate elements,” in: Computations in Algebra and Combinatorics. Application in Algebra and Combinatorial Theoretic Investigations, Kiev (1978), pp. 165–190.
A. S. Kondrat'ev, “Finite simple groups whose Sylow 2-subgroup is an extension of an Abelian group by means of a group of rank 1,” Algebra Logika,14, No. 3, 288–303 (1975).
A. S. Kondrat'ev, “Finite simple groups whose Sylow 2-subgroups have a cyclic commutant,” Sib. Mat. Zh.,17, No. 1, 86–90 (1976).
A. S. Kondrat'ev, “Finite nonprimary groups with complementable biprimary subgroups of even order,” Mat. Zap. Ural'sk. Univ.,9, No. 3, 44–52 (1975).
A. S. Kondrat'ev, “Finite simple groups with Sylow 2-subgroups of order 27,” Izv. AN SSSR, Ser. Mat.,41, No. 4, 752–767 (1977).
A. S. Kondrat'ev, “Finite groups whose Sylow 2-subgroup contains an elementary Abelian subgroup of index 4,” Algebra Logika,16, No. 5, 557–576 (1977).
A. S. Kondrat'ev, “Some remarks on finite groups with a decomposalbe Sylow 2-subgroup,” Sib. Mat. Zh.,20, No. 3, 665–666 (1979).
A. S. Kondrat'ev, “Finite groups with a Sylow 2-subgroup having an elementary commutant of order 8,” Mat. Zametki,27, No. 5, 673–681 (1980).
A. S. Kondrat'ev, “Sylow 2-subgroups of finite nonsolvable groups,” in: 6th All-Union Symposium on Group Theory, Kiev, 1980, pp. 69–81.
A. S. Kondrat'ev, “On 2-local subgroups of finite groups,” Algebra Logika,21, No. 2, 178–192 (1982).
A. S. Kondrat'ev, “On solvable 2-local subgroups of finite groups,” Algebra Logika,21, No. 6, 670–689 (1982).
A. S. Kondrat'ev, “Finite groups whose Sylow 2-subgroups possess a Hamiltonian maximal subgroup,” Mat. Zap. Ural'sk. Univ.,13, No. 3, 81–86 (1983).
N. P. Kontorovich and V. T. Nagrebetskii, “On finite minimal groups which are not p-supersolvable,” Mat. Zap. Ural'sk. Univ.,9, No. 3, 53–59 (1975).
Yu. A. Korzyukov, “Finite. ¯cN-groups,” Uch. Zap. Perm. Univ., No. 343, 48–52 (1975).
Yu. A. Korzyukov, “Finite ssN-groups. I,” Questions of Group Theory and Homological Algebra, Yaroslavl' (1981), pp. 57–62; II (1982), pp. 141–142.
L. F. Kosvintsev and V. M. Sosnin, “On the connectivity of the graph of intersections of maximal subgroups of a finite group,” Preprint, Perm Univ. (1980).
L. F. Kosvintsev and V. M. Sosnin, “On a finite group in which each proper subgroup of composite order has a nonconnected graph of intersections of subgroups,” Preprint, Perm Univ., (1980).
I. F. Kosvintsev and V. M. Sosnin, “On a class of finite groups with a restriction on the maximal subgroups,” Preprint, Perm Univ. (1981).
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Translated from Itogi Nauki i Tekhniki, Seriya Algebra, Topologiya, Geometriya, Vol. 24, pp. 3–120, 1986.
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Kondrat'ev, A.S., Makhnev, A.A. & Starostin, A.I. Finite groups. J Math Sci 44, 237–318 (1989). https://doi.org/10.1007/BF01676868
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DOI: https://doi.org/10.1007/BF01676868