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Sibirsk. Mat. Zh., 2017, Volume 58, Number 3, Pages 526–529 (Mi smj2877)  

A characterizing property of CP-groups

A. A. Buturlakinab, R. Shenc, W. Shid

a Sobolev Institute of Mathematics, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia
c Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei Province, P. R. China
d Department of Mathematics, Chongqing University of Arts and Sciences, Yongchuan, Chongqing, P. R. China

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.

Funding Agency Grant Number
National Natural Science Foundation of China 11561021
11671063
Innovation Foundation of Chongqing KJTD201321
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).


DOI: https://doi.org/10.17377/smzh.2017.58.304

Full text: PDF file (245 kB)
References: PDF file   HTML file

English version:
Siberian Mathematical Journal, 2017, 58:3, 405–407

Bibliographic databases:

UDC: 512.542
MSC: 20D45
Received: 23.06.2016

Citation: A. A. Buturlakin, R. Shen, W. Shi, “A characterizing property of CP-groups”, Sibirsk. Mat. Zh., 58:3 (2017), 526–529; Siberian Math. J., 58:3 (2017), 405–407

Citation in format AMSBIB
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