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On the minimality property for locally finite groups

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Literature cited

  1. S. N. Chernikov, "Infinite special groups," Matem. Sb.,6, No. 2 (1939).

  2. S. N. Chernikov, "Infinite locally solvable groups," Matem. Sb.,7, No. 1 (1940).

  3. S. N. Chernikov, "On the theory of infinite special groups," Matem. Sb.,7, No. 3 (1940).

  4. S. N. Chernikov, "Finiteness conditions in the general theory of groups," Usp. Matem. Nauk,14, No. 5 (1959).

  5. P. S. Novikov and S. I. Adyan, "Infinite periodic groups," Izv. Akad. Nauk SSSR, Ser. Mat.,32, Nos. 1, 2, 3 (1968).

  6. P. S. Novikov and S. I. Adyan, "On commutative subgroups and the conjugacy problem in free periodic groups of odd order," Izv. Akad. Nauk SSSR, Ser. Mat.,32, No. 5 (1968).

  7. M. I. Kargapolov, "On a problem of O. Yu. Schmidt," Sib. Matem. Zh.,4, 233–235 (1963).

    Google Scholar 

  8. W. Feit and J. Thompson, "Solvability of groups of odd order," Pacif. J. Math.,13, 775–1029 (1963).

    Google Scholar 

  9. Amsterdam Mathematics Congress, 1954, Moscow (1959).

  10. P. Hall and C. R. Kylatilaka, "A property of locally finite groups," J. London Math. Soc.,39, 235–239 (1964).

    Google Scholar 

  11. S. P. Strunkov, "Normalizers and Abelian subgroups of some group classes," Izv. Akad. Nauk SSSR, Ser. Mat.,31, No. 4, 657–670 (1967).

    Google Scholar 

  12. V. P. Shunkov, "On some generalization of the Frobenius theorem to periodic groups," Algebra i Logika,6, No. 3, 113–123 (1967).

    Google Scholar 

  13. V. P. Shunkov, "On a locally finite group with extremal Sylow p-subgroups in some prime p," Sib. Matem. Zh.,8, No. 1, 213–229 (1967).

    Google Scholar 

  14. V. P. Shunkov, "On the theory of locally finite groups," Dokl. Akad. Nauk SSSR,168, 1272–1274 (1966).

    Google Scholar 

  15. V. P. Shunkov, "On an abstract characterization of a simple projective group of type PGL(2, k) over a field K of characteristic r ⊋ 0, 2," Dokl. Akad. Nauk SSSR,163, 837–849 (1965).

    Google Scholar 

  16. V. P. Shunkov, "On the minimality problem for subgroups in locally finite groups," Dokl. Akad. Nauk SSSR,181, 294–295 (1968).

    Google Scholar 

  17. G. Higman, "Suzuki 2-groups," Ill. J. Math.,7, 79–96 (1963).

    Google Scholar 

  18. A. G. Kurosh, Theory of Groups [in Russian], Nauka (1967).

  19. N. Blackburn, "Some remarks on Cernikov p-groups," Ill. J. Math.,6, 421–433 (1962).

    Google Scholar 

  20. R. Brauer, "Some application of the theory of blocks of characters of finite groups. I, II," J. Algebra,1, 152–167, 307–334 (1964).

    Google Scholar 

  21. D. Gorenstein, Finite Groups, New York (1968).

  22. G. Glauberman, "Central elements in core-free groups," J. Algebra,4, 403–420 (1966).

    Google Scholar 

  23. H. Bender, Finite Groups Having a Strongly Embedded Subgroup. A Symposium on the Theory of Finite Groups (ed. R. Brauer and C.-H. Sah), Benjamin (1969).

  24. J. Alperin, On Groups with Quasi-Dihedral Sylow 2-Subgroups. A Symposium on the Theory of Finite Groups (ed. R. Brauer and C. H. Sah), Benjamin (1969).

  25. M. Hall, Theory of Groups, Macmillan (1961).

  26. V. P. Shunkov, "On the theory of generalized solvable groups," Dokl. Akad. Nauk SSSR,160, 1279–1282 (1965).

    Google Scholar 

  27. R. Brauer and M. Suzuki, "On finite groups of even order whose 2-Sylow groups are a quaternion," Proc. Mat. Acad. Sci. USA,45, 403–420 (1966).

    Google Scholar 

  28. H. Hasse, Lectures on Number Theory [Russian translation], IL (1953).

  29. Z. Janko and J. G. Thompson, "On finite simple groups whose Sylow 2-subgroups have no normal elementary subgroups of order 8," Math. Z.,113, No. 5, 385–397 (1970).

    Google Scholar 

  30. V. P. Shunkov, Groups with Finiteness Conditions. Tenth All-Union Algebraic Colloquium. Resume of Reports and Notes [in Russian], Novosibirsk, Vol. 1 (1969), p. 35.

    Google Scholar 

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Translated from Algebra i Logika, Vol. 9, No. 2, pp. 220–248, March–April, 1970.

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Shunkov, V.P. On the minimality property for locally finite groups. Algebr Logic 9, 137–151 (1970). https://doi.org/10.1007/BF02218982

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