On g-s-supplemented subgroups of finite groups

doi:10.1007/s11464-010-0006-8

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Front. Math. China ›› 2010, Vol. 5 ›› Issue (2) : 287-295. DOI: 10.1007/s11464-010-0006-8

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On g-s-supplemented subgroups of finite groups

Wenbin GUO¹,Fengyan XIE²,Yi LU³,

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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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Wenbin GUO, Fengyan XIE, Yi LU,. On g-s-supplemented subgroups of finite groups. Front. Math. China, 2010, 5(2): 287‒295 https://doi.org/10.1007/s11464-010-0006-8