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On groups whose element orders divide 6 and 7

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Abstract

We prove that a group whose element orders divide 6 and 7 either is locally finite or an extension of a nontrivial elementary abelian 2-group by a group without involutions.

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References

  1. Lytkina D. and Mazurov V., “Groups with given element orders,” J. Sib. Fed. Univ. Math. Phys., vol. 7, no. 2, 191–203 (2014).

    Google Scholar 

  2. Hall M., “Solution of the Burnside problem for exponent six,” Illinois J. Math., vol. 2, 764–786 (1958).

    MathSciNet  MATH  Google Scholar 

  3. Mazurov V. D. and Mamontov A. S., “On periodic groups with small orders of elements,” Sib. Math. J., vol. 50, no. 2, 316–321 (2009).

    Article  MathSciNet  MATH  Google Scholar 

  4. Jabara E., “Fixed point free action of groups of exponent 5,” J. Austral. Math. Soc., vol. 77, 297–304 (2004).

    Article  MathSciNet  MATH  Google Scholar 

  5. GAP—Groups, Algorithms, and Programming, vers. 4.6.5 (2013); http://www.gap-system.org.

  6. Williams J. S., “Prime graph components of finite groups,” J. Algebra, vol. 69, no. 2, 487–513 (1981).

    Article  MathSciNet  MATH  Google Scholar 

  7. Mazurov V. D., “Recognition of finite simple groups S4(q) by their element orders,” Algebra and Logic, vol. 41, no. 2, 93–110 (2002).

    Article  MathSciNet  Google Scholar 

  8. Lytkina D. V., Mazurov V. D., Mamontov A. S., and Jabara E., “Groups whose element orders do not exceed 6,” Algebra and Logic, vol. 53, no. 5, 365–376 (2014).

    Article  MathSciNet  MATH  Google Scholar 

  9. Shunkov V. P., “On periodic groups with an almost regular involution,” Algebra and Logic, vol. 11, no. 4, 260–272 (1972).

    Article  MathSciNet  MATH  Google Scholar 

  10. Mamontov A. S., “Groups of exponent 12 without elements of order 12,” Sib. Math. J., vol. 54, no. 1, 114–118 (2013).

    Article  MathSciNet  MATH  Google Scholar 

  11. Mazurov V. D., “Infinite groups with Abelian centralizers of involutions,” Algebra and Logic, vol. 39, no. 1, 42–49 (2000).

    Article  MathSciNet  MATH  Google Scholar 

  12. Kargapolov M. I. and Merzlyakov Yu. I., Fundamentals of the Theory of Groups, Springer-Verlag, New York, Heidelberg, and Berlin (1979).

    Book  MATH  Google Scholar 

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Authors and Affiliations

  1. University of Science and Technology of China, School of Mathematical Science, Hefei, P. R. China

    W. Guo

  2. Sobolev Institute of Mathematics, Novosibirsk State University, Novosibirsk, Russia

    A. S. Mamontov

Authors
  1. W. Guo
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  2. A. S. Mamontov
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Corresponding author

Correspondence to W. Guo.

Additional information

The first author was supported by the NNSF of China (11371335) and the Wu Wen-Tsuu Key Laboratory of Mathematics of the Chinese Academy of Science.

Hefei; Novosibirsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 58, No. 1, pp. 88–94, January–February, 2017; DOI: 10.17377/smzh.2017.58.109.

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Guo, W., Mamontov, A.S. On groups whose element orders divide 6 and 7. Sib Math J 58, 67–71 (2017). https://doi.org/10.1134/S0037446617010098

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  • DOI: https://doi.org/10.1134/S0037446617010098

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