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Siberian Mathematical Journal

, Volume 58, Issue 3, pp 405–407 | Cite as

A characterizing property of CP-groups

  • A. A. ButurlakinEmail author
  • R. Shen
  • W. Shi
Article
  • 51 Downloads

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.

Keywords

finite groups CP-groups elements of prime power order 

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Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsNovosibirsk State UniversityNovosibirskRussia
  2. 2.Department of MathematicsHubei University for NationalitiesEnshi, Hubei ProvinceP. R. China
  3. 3.Department of MathematicsChongqing University of Arts and SciencesYongchuan, ChongqingP. R. China

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