On g-s-supplemented subgroups of finite groups

Abstract

A subgroup H of a group G is said to be g-s-supplemented in G if there exists a subgroup K of G such that HK⊴G and H ∩ K ⩽ H_sG, where H_sG is the largest s-permutable subgroup of G contained in H. By using this new concept, we establish some new criteria for a group G to be soluble.

Keywords

Finite group / g-s-supplemented subgroup / Sylow subgroup / soluble group

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