journal article
oaidoi:10.1016/j.jalgebra.2007.02.053

Bounds in groups with trivial Frattini subgroup

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Publication date
1 February 2008
Publisher
Elsevier Inc.
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    Abstract

    AbstractLet G be an arbitrary group with finite commutator subgroup G′. We prove that if the Frattini subgroup Φ(G) is trivial then |G:Z(G)|⩽|G′|2, and this estimate is sharp. A special case of this result was conjectured by M. Herzog, G. Kaplan and A. Lev

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