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A characterizing property of CP-groups

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Abstract

Let G be a finite group. It is proved that if, for every prime p, the number of nonidentity p-elements of G is divisible by the p′-part of |G|, then all element orders of G are prime powers.

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Author information

Authors and Affiliations

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

    A. A. Buturlakin

  2. Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei Province, P. R. China

    R. Shen

  3. Department of Mathematics, Chongqing University of Arts and Sciences, Yongchuan, Chongqing, P. R. China

    W. Shi

Authors
  1. A. A. Buturlakin
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  2. R. Shen
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  3. W. Shi
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Corresponding author

Correspondence to A. A. Buturlakin.

Additional information

The second author was supported by the NSFC (Grant 11561021) and the third author was supported by the NSFC (Grant 11671063) and the Innovation Foundation of Chongqing (KJTD201321).

Original Russian Text Copyright © 2017 Buturlakin A.A., Shen R., and Shi W.

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Buturlakin, A.A., Shen, R. & Shi, W. A characterizing property of CP-groups. Sib Math J 58, 405–407 (2017). https://doi.org/10.1134/S0037446617030041

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  • DOI: https://doi.org/10.1134/S0037446617030041

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