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On groups with a strongly imbedded subgroup having an almost layer-finite periodic part

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Ukrainian Mathematical Journal Aims and scope

We study Shunkov groups with the following condition: the normalizer of any finite nontrivial subgroup has an almost layer-finite periodic part. It is proved that such a group has an almost layer-finite periodic part if it has a strongly imbedded subgroup with almost layer-finite periodic part.

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References

  1. S. N. Chernikov, “On the theory of infinite p-groups,” Dokl. Akad. Nauk SSSR, 71–74 (1945).

  2. A. N. Izmailov and V. P. Shunkov, “Two criteria for nonsimplicity of a group with infinitely isolated subgroup,” Alg. Logika, 21, No. 6, 647–669 (1982).

    MathSciNet  Google Scholar 

  3. A. N. Izmailov, “On a strongly imbedded infinitely isolated subgroup in a periodic group,” Alg. Logika, 22, No. 2, 128–137 (1983).

    MathSciNet  Google Scholar 

  4. V. D. Mazurov, “On twice transitive groups of substitutions,” Sib. Mat. Zh., 31, No. 4, 102–104 (1990).

    MathSciNet  Google Scholar 

  5. V. D. Mazurov, “On infinite groups with Abelian centralizers of involutions,” Alg. Logika, 39, No. 1, 74–86 (2000).

    MathSciNet  MATH  Google Scholar 

  6. A. I. Sozutov, “On infinite groups with strongly imbedded subgroup,” Alg. Logika, 39, No. 5, 602–617 (2000).

    MathSciNet  Google Scholar 

  7. A. I. Sozutov and N. M. Suchkov, “On infinite groups with a given strongly isolated 2-subgroup,” Mat. Zametki, 68, Issue 2, 272–285 (2000).

    Article  MathSciNet  Google Scholar 

  8. A. I. Sozutov, “Two criteria for nonsimplicity of a group with strongly imbedded subgroup and finite involution,” Mat. Zametki, 69, Issue 3, 443–453 (2001).

    Article  MathSciNet  Google Scholar 

  9. N. M. Suchkov, “On periodic groups with Abelian centralizers of involutions,” Mat. Sb., 193, No. 2, 153–160 (2002).

    Article  MathSciNet  Google Scholar 

  10. V. I. Senashov, “Sufficient conditions for the almost layer finiteness of groups,” Ukr. Mat. Zh., 51, No. 4, 472–485 (1999); English translation: Ukr. Math. J., No. 4, 525–537 (1999).

    Article  MathSciNet  MATH  Google Scholar 

  11. V. I. Senashov, “Structure of an infinite Sylow subgroup in some periodic Shunkov groups,” Diskr. Mat., 14, No. 4, 133–152 (2002).

    Article  MathSciNet  Google Scholar 

  12. V. I. Senashov, “On Shunkov groups with strongly imbedded subgroup” Tr. Inst. Mat. Mekh. Ural. Otd. Ros. Akad. Nauk, 15, No. 2, 203–210 (2009).

    Google Scholar 

  13. V. I. Senashov, “On Shunkov groups with strongly imbedded almost layer-finite subgroup” Tr. Inst. Mat. Mekh. Ural. Otd. Ros. Akad. Nauk, 16, No. 3, 234–239 (2010).

    Google Scholar 

  14. V. I. Senashov and V. P. Shunkov, “Almost layer-finiteness of the periodic part of an involution-free group,” Diskr. Mat., 15, No. 3, 91–104 (2003).

    Article  MathSciNet  Google Scholar 

  15. V. I. Senashov, “Groups satisfying the minimality condition for non-almost-layer-finite subgroups,” Ukr. Mat. Zh., 43, No. 7–8, 1002–1008 (1991); English translation: Ukr. Math. J., 43, No. 7–8, 935–941 (1991).

    MathSciNet  Google Scholar 

  16. S. N. Chernikov, Groups with Given Properties of a System of Subgroups [in Russian], Nauka, Moscow (1980).

    Google Scholar 

  17. N. G. Suchkova and V. P. Shunkov, “On groups with minimality condition for Abelian subgroups,” Alg. Logika, 26, No. 4, 445–469 (1986).

    MathSciNet  Google Scholar 

  18. V. P. Shunkov, T 0-Groups [in Russian], Nauka, Moscow (2000).

    Google Scholar 

  19. V. P. Shunkov, M p -Groups [in Russian], Nauka, Moscow (1990).

    Google Scholar 

  20. M. I. Kargapolov and Yu. I. Merzlyakov, Foundations of the Theory of Groups [in Russian], Nauka, Moscow (1982).

    Google Scholar 

  21. V. P. Shunkov, On Imbedding of Primary Elements in a Group [in Russian], Nauka, Novosibirsk (1992).

    Google Scholar 

  22. A. I. Sozutov and V. P. Shunkov, “On infinite groups saturated with Frobenius subgroups,” Alg. Logika, 16, No. 6, 711–735 (1977); 18, No. 2, 206–223 (1979).

    MathSciNet  Google Scholar 

  23. A. M. Popov, A. I. Sozutov, and V. P. Shunkov, Groups with Systems of Frobenius Subgroups [in Russian], Krasnoyarsk State Technical University, Krasnoyarsk (2004).

  24. A. G. Kurosh, The Theory of Groups [in Russian], Nauka, Moscow (1967); English translation: AMS Chelsea Publishing, Providence, RI (2003).

    Google Scholar 

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, No. 3, pp. 384–391, March, 2012.

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Senashov, V.I. On groups with a strongly imbedded subgroup having an almost layer-finite periodic part. Ukr Math J 64, 433–440 (2012). https://doi.org/10.1007/s11253-012-0656-7

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  • DOI: https://doi.org/10.1007/s11253-012-0656-7

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