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Structure of a group with elements of order at most 4

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Abstract

We prove that every group in which the order of each element is at most 4 either possesses a nontrivial class 2 nilpotent normal Sylow subgroup or includes a normal elementary abelian 2-subgroup the quotient by which is isomorphic to the nonabelian group of order 6.

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References

  1. Sanov I. N., “Solution of the Burnside problem for the exponent 4,” Leningrad. Gos. Univ. Uchen. Zap. Ser. Mat. Nauk, No. 55, 166–170 (1940).

  2. Thompson J. G., “Finite groups with fixed-point-free automorphisms of prime order,” Proc. Nat. Acad. Sci. USA, 45, 578–581 (1959).

    Article  MATH  Google Scholar 

  3. Gorenstein D., Finite Groups, Harper & Row, New York (1973).

    Google Scholar 

  4. Neumann B. H., “Groups with automorphisms that leave the neutral element fixed,” Arch. Math., 7, 1–5 (1956).

    Article  MATH  MathSciNet  Google Scholar 

  5. Hall M., The Theory of Groups [Russian translation], Izdat. Inostr. Lit., Moscow (1962).

    MATH  Google Scholar 

  6. Zavarnitsin A. V. and Mazurov V. D., “On the orders of elements in coverings of symmetric and alternating groups,” Algebra i Logika, 38, No. 3, 296–315 (1999).

    MathSciNet  Google Scholar 

  7. Lytkina D. V., “Structure of a group with elements of order at most 4,” in: Mathematical Systems, Krasnoyarsk Univ., Krasnoyarsk, 2005, No. 4, pp. 54–59.

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Authors and Affiliations

  1. Siberian Foundation for Algebra and Logic, Novosibirsk, Russia

    D. V. Lytkina

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  1. D. V. Lytkina
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Original Russian Text Copyright © 2007 Lytkina D. V.

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 48, No. 2, pp. 353–358, March–April, 2007.

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Lytkina, D.V. Structure of a group with elements of order at most 4. Sib Math J 48, 283–287 (2007). https://doi.org/10.1007/s11202-007-0028-y

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  • DOI: https://doi.org/10.1007/s11202-007-0028-y

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