On an inverse problem to Frobenius' theorem

被引：9

作者：

Meng, Wei ^{[1
]}

Shi, Jiangtao ^{[2
,3
]}

机构：

[1] Yunnan Univ Nationalities, Sch Math & Comp Sci, Kunming 650031, Yunnan, Peoples R China

[2] Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China

[3] Peking Univ, LMAM, Beijing 100871, Peoples R China

来源：

ARCHIV DER MATHEMATIK | 2011年 / 96卷 / 02期

基金：

中国博士后科学基金; 中国国家自然科学基金;

关键词：

Frobenius' theorem; p-group; Nilpotent group; SPORADIC SIMPLE-GROUPS; LIE TYPE; CONJECTURE;

D O I：

10.1007/s00013-010-0211-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G be a finite group and e a positive integer dividing vertical bar G vertical bar, the order of G. Denoting L(c)(G) = {x is an element of G vertical bar x(c) = 1}, Frobenius proved that vertical bar L(e)(G)vertical bar = ke for a positive integer k >= 1. In this paper, we give a complete classification of finite groups G with vertical bar L(e)(G)vertical bar <= 2e for every e dividing vertical bar G vertical bar.

引用

页码：109 / 114

页数：6

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