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A group with H-Frobenius element of even order

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Abstract

We settle Question 10.61 in the Kourovka Notebook for the case where the order of an element a is even.

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REFERENCES

  1. A. I. Sozutov and V. P. Shunkov, “A generalization of the Frobenius theorem to infinite groups,” Mat. Sb., 100, No. 4, 495–506 (1976).

    Google Scholar 

  2. Yu. M. Gorchakov, “Infinite Frobenius groups,” Algebra Logika, 4, No. 1, 15–29 (1965).

    Google Scholar 

  3. A. I. Sozutov, “Groups with a class of Frobenius-Abelian elements,” Algebra Logika, 34, No. 5, 531–549 (1995).

    Google Scholar 

  4. B. Fisher, “Frobenius automorphismen endligher Gruppen,” Math. Ann., 163, No. 4, 273–298 (1966).

    Google Scholar 

  5. M. Aschbacher, “A characterization of certain Frobenius groups,” Ill. J. Math, 18, No. 3, 418–426 (1974).

    Google Scholar 

  6. V. P. Shunkov, “A non-simplicity criterion for groups,” Algebra Logika, 14, No. 5, 491–522 (1975).

    Google Scholar 

  7. A. I. Sozutov, “Groups with Frobenius pairs of conjugate elements,” Algebra Logika, 16, No. 2, 204–212 (1977).

    Google Scholar 

  8. A. I. Sozutov and V. P. Shunkov, “Infinite groups saturated with Frobenius subgroups,” Algebra Logika, 16, No. 6, 711–735 (1977).

    Google Scholar 

  9. A. I. Sozutov and V. P. Shunkov, “Infinite groups saturated with Frobenius subgroups. II,” Algebra Logika, 18, No. 2, 206–223 (1979).

    Google Scholar 

  10. V. M. Busarkin and Yu. M. Gorchakov, Finite Groups That Admit Partitions [in Russian], Nauka, Moscow (1968).

    Google Scholar 

  11. A. I. Starostin, “Frobenius groups,” Ukr. Mat. Zh., 23, No. 5, 629–639 (1971).

    Google Scholar 

  12. The Kourovka Notebook, Unsolved Problems in Group Theory, 15th edn., Institute of Mathematics SO RAN, Novosibirsk (2002).

  13. A. M. Popov, “A criterion for non-simplicity of groups with involutions,” Algebra Logika, 42, No. 2, 227–236 (2003).

    Google Scholar 

  14. A. M. Popov, “The structure of some groups with finite H-Frobenius elements,” Algebra Logika, 43, No. 2, 220–228 (2004).

    Google Scholar 

  15. A. Kh. Zhurtov and V. D. Mazurov, “Frobenius groups generated by quadratic elements,” Algebra Logika, 42, No. 3, 271–292 (2003).

    Google Scholar 

  16. A. M. Popov, “On groups with Frobenius elements,” Proc. Int. Conf. “Algebra and Its Applications,” Krasnoyarsk, 2002, to appear.

  17. A. I. Sozutov, “The structure of a complement in some Frobenius groups,” Sib. Mat. Zh., 35, No. 4, 893–901 (1994).

    Google Scholar 

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

    Google Scholar 

  19. M. Hall, The Theory of Groups, Macmillan, New York (1959).

    Google Scholar 

  20. M. I. Kargapolov and Yu. I. Merzlyakov, Fundamentals of Group Theory [in Russian], 2nd edn., Nauka, Moscow (1977).

    Google Scholar 

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Authors
  1. A. M. Popov
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  2. A. I. Sozutov
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Additional information

Supported by RFBR grant No. 03-01-00356 and by the Krasnoyarsk Science Foundation, project 11F0202C.

Translated from Algebra i Logika, Vol. 44, No. 1, pp. 70–80, January–February, 2005.

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Popov, A.M., Sozutov, A.I. A group with H-Frobenius element of even order. Algebr Logic 44, 40–45 (2005). https://doi.org/10.1007/s10469-005-0005-0

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  • DOI: https://doi.org/10.1007/s10469-005-0005-0

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