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
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
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页码:893 / 896
页数:4
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