The Intersection Of Maximal Subgroups Which Are Not Minimal Non-abelian In A Finite P-group

Posted on:2015-02-15

Degree:Master

Type:Thesis

Country:China

Candidate:J Yuan

Full Text:PDF

GTID:2250330428463452

Subject:Basic mathematics

Abstract/Summary:

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Let G be a finite p-groups and ΦNA1M(G) the intersection of all maxi-mal subgroups which are not minimal non-abelian in G.This paper proves|G:ΦN.A1A,M(G)|≤p3and classify fmite p-groups with|G:ΦN.A1M(G)|p,p2and p3,respectivel y. As a corollary,This solves a problem proposed by Berkovich and Janko in their book "Groups of Prime Power of Order Vol.3"...

Keywords/Search Tags:

finite p-groups, minimal non-abelian p-groups, the inter-section of maximal subgroups which are not minimal non-abelian

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