Title: Finite Non-abelian Simple Groups Which Contain a Non-trivial Semipermutable Subgroup
Abstract: A subgroup H of a group G is called semipermutable if it is permutable with every subgroup K of G with (|H|,|K|)=1, and s-semipermutable if it is permutable with every Sylow p-subgroup of G with (p,|H|)=1. In this paper, we classify all finite non-abelian simple groups which contain a non-trivial semipermutable (s-semipermutable) subgroup. As a corollary of our main result, we give a complete answer to an unsolved problem in group theory proposed by V.S. Monakhov in 1990.
Publication Year: 2005
Publication Date: 2005-06-01
Language: en
Type: article
Indexed In: ['crossref']
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Cited By Count: 5
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