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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Bibliographische Detailangaben
Veröffentlicht in:	Siberian mathematical journal 2017-05, Vol.58 (3), p.405-407
Hauptverfasser:	Buturlakin, A. A., Shen, R., Shi, W.
Format:	Artikel
Sprache:	eng
Schlagworte:	Mathematics Mathematics and Statistics
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	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