A criterion for p-nilpotency and p-closedness by the sum of element orders

被引：5
作者：
Baniasad Azad, Morteza [1 ]
Khosravi, Behrooz [1 ]
机构：
[1] Amirkabir Univ Technol, Tehran Polytech, Fac Math & Comp Sci, Dept Pure Math, 424 Hafez Ave, Tehran 15914, Iran
来源：
COMMUNICATIONS IN ALGEBRA | 2020年 / 48卷 / 12期
关键词：
Sum of element orders; p-closedness; p-nilpotency; supersolvable; POWER GRAPHS;
D O I：
10.1080/00927872.2020.1788571
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
LetGbe a finite group,psi(G)= n-ary sumation g is an element of Go(g)and psi ''(G)=psi(G)/|G|2,whereo(g) denotes the order ofg. In this paper, we prove that ifpis a prime number and psi ''(G)>(p2+p+1)/(4p2),thenG=Op(G)xOp '(G),whereOp(G)is cyclic. In addition,Gis supersolvable andG ''<= Z(G).
引用
收藏
页码：5391 / 5395
页数：5
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