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Finite irreducible subgroups of the group GL(n,Z)

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Literature Cited

  1. H. Zassenhaus, “Über einen Algorithmus zur Bestimmung der Raumgruppen,” Comment. Math. Helv.,21, 117–141 (1948).

    Google Scholar 

  2. H. Broun, J. Neubuser, and H. Zassenhaus, “On integral groups. I–III, “Numer. Math., No. 19, 386–399; No. 20, 22–31 (1972); Math. Comput., No. 27, 167–182 (1973).

    Google Scholar 

  3. S. S. Ryshkov, “Maximal finite groups of integral n×n-matrices and complete groups of integral automorphisms of positive quadratic forms (of Brave type),” Tr. Mat. Inst. Akad. Nauk SSSR,128, 183–211 (1972).

    Google Scholar 

  4. W. Plesken and M. Pohst, “On maximal finite irreducible subgroups of GL(n, Z),” Math. Comput., No. 31, 536–573 (1977); No. 34, 245–301 (1980).

    Google Scholar 

  5. D. A. suprunenko, “Finite irreducible solvable linear groups,” Izv. Akad. Nauk BSSR, Ser. Fiz.-Mat. Nauk, No. 3, 5–16 (1971).

    Google Scholar 

  6. T. I. Kopylova, “Finite irreducible solable groups of matrices of prime degree,” Izv. Akad. Nauk BSSR, Ser. Fiz.-Mat. Nauk, No. 5, 14–22 (1976).

    Google Scholar 

  7. D. A. Suprunenko, “Minimal irreducible solvable linear groups of prime degree,” Tr. Mosk. Mat. O-va.,29, 233–234 (1973).

    Google Scholar 

  8. V. P. Platonov, “Finiteness of minimal irreducible linear groups,” Izv. Akad. Nauk BSSR, Ser. Fiz.-Mat. Nauk, No. 5, 96–97 (1975).

    Google Scholar 

  9. D. A. Suprunenko, “Real minimal irreducible matrix groups,” Dokl. Akad. Nauk SSR,283, No. 3, 29–32 (1978).

    Google Scholar 

  10. T. I. Kopylova, “Minimal irreducible solvable nonnilpotent linear groups of degree p2,” Minsk (1979) [Preprint/Akad. Nauk BSSR, Inst. Mat., No. 18 (50)].

  11. A. A. Kirilyuk and V. P. Rud'ko, “Finite irreducible solvable subgroups of the group GL(p, Z),” Dokl. Akad. Nauk UkrSSR, Ser. A, No. 8, 17–20 (1980).

    Google Scholar 

  12. P. M. Gudivok, A. A. Kirilyuk, V. P. Rud'ko, and A. I. Tsitkin, “Finite subgroups of the group GL(n, Z),” Kibernetika, No. 6, 71–82 (1982).

    Google Scholar 

  13. C. Curtis and I. Reiner, Theory of Representations of Finite Grups and Associative Algebras [Russian translation], Nauka, Moscow (1969).

    Google Scholar 

  14. D. Polya, “Combinatorial calculations for graph groups and chemical compounds,” in: Listed Problems of Combinatorial Analysis [Russian translation], Mir, Moscow (1979), pp. 36–136.

    Google Scholar 

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Authors
  1. P. M. Gudivok
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  2. Yu. V. Kapitonova
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  3. V. P. Rud'ko
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Additional information

Translated from Kibernetika, No. 5, pp. 1–16, September–October, 1986.

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Gudivok, P.M., Kapitonova, Y.V. & Rud'ko, V.P. Finite irreducible subgroups of the group GL(n,Z). Cybern Syst Anal 22, 535–553 (1986). https://doi.org/10.1007/BF01068349

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  • DOI: https://doi.org/10.1007/BF01068349

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