On weakly s-permutable subgroups of finite groups

Abstract Let G be a finite group, H a subgroup of G and H s G the subgroup of H generated by all those subgroups of H which are s-permutable in G. Then we say that H is weakly s-permutable in G if G has a subnormal subgroup T such that H T = G and T ∩ H ⩽ H s G . We fix in every non-cyclic Sylow subgroup P of G a subgroup D satisfying 1 | D | | P | and study the structure of G under the assumption that all subgroups H with | H | = | D | are weakly s-permutable in G.

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