Recognition of some finite simple groups by the orders of vanishing elements

被引：1

作者：

Liu, Dandan ^{[1
]}

Zhang, Jinshan ^{[1
]}

机构：

[1] Sichuan Univ Sci & Engn, Sch Sci, Zigong 643000, Peoples R China

来源：

PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES | 2021年 / 131卷 / 01期

关键词：

Finite groups; characters; vanishing elements; 20C15;

D O I：

10.1007/s12044-020-00603-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G be a finite group. A vanishing element of G is an element g is an element of G such that chi (g)=0 for some irreducible complex character chi of G. Denote by Vo(G) the set of the orders of vanishing elements of G. A finite group all of whose elements have prime power order is called a CP-group. Generally, a finite group G is called a VCP-group if every element in Vo(G) is a prime power. Here, we classify completely the non-solvable VCP-groups and show that, except for A7, the non-solvable VCP-groups coincide with the non-solvable CP-groups. Moreover, as a consequence, we give a new characterization of the simple VCP-groups, namely, if G is a finite group and M is a finite non-abelian simple VCP-group except for L2(9) such that Vo(G)=Vo(M), then GM. In addition, we also prove that if Vo(G)=Vo(L2(9)), then either GL2(9), or GNA, where ASL2(4) and N is an elementary abelian 2-group and a direct sum of natural SL2(4)-modules.

引用

页数：9

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