A characterizing property of CP-groups

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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Bibliographic Details
Published in:Siberian mathematical journal 2017-05, Vol.58 (3), p.405-407
Main Authors: Buturlakin, A. A., Shen, R., Shi, W.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary: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.
ISSN:0037-4466
1573-9260
DOI:10.1134/S0037446617030041