On a question of L.A. Shemetkov concerning the intersection of \cal F-maximal subgroups of finite groups

2011/03/24 by Alexander N. Skiba, Skiba, Alexander N. · 1 citation
Mathematics · #20D10 #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:20D10

paper · pdf · doi:10.48550/arxiv.1103.4729

arxiv created 2011/03/24 · arxiv updated 2011/03/25

Abstract

We investigate the influence of the intersection of the \cal F-maximal subgroups on the structure of a finite group. In particular, answering a question of L.A Shemetkov we give conditions under which a hereditary saturated formation \cal F has a property that for any finite group G, the \cal F-hypercentre of G coincides with the intersection of all \cal F-maximal subgroups of G.

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• On the intersection of the \cal F-maximal subgroups and the generalized \cal F-hypercentre of a finite group

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