Bounds in groups with trivial Frattini subgroup

被引：4

作者：

Halasi, Z. ^{[1
]}

Podoski, K. ^{[2
]}

机构：

[1] Cent European Univ, Dept Math & Its Applicat, H-1051 Budapest, Hungary

[2] Hungarian Acad Sci, Alfred Renyi Inst Math, H-1364 Budapest, Hungary

来源：

JOURNAL OF ALGEBRA | 2008年 / 319卷 / 03期

关键词：

index of the centre; commutator subgroup; Frattini subgroup; primitive permutation group;

D O I：

10.1016/j.jalgebra.2007.02.053

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G be an arbitrary group with finite commutator subgroup G '. We prove that if the Frattini subgroup Phi (G) is trivial then vertical bar G : Z(G)vertical bar <= vertical bar G 'vertical bar(2), and this estimate is sharp. A special case of this result was conjectured by M. Herzog, G. Kaplan and A. Lev. (c) 2007 Elsevier Inc. All rights reserved.

引用

页码：893 / 896

页数：4

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