On ss-quasinormal and weakly s-supplemented subgroups of finite groups

Assume that G is a finite group and H is a subgroup of G: A subgroup H is called ss-quasinormal in G if there is a subgroup B of G such that G = HB and H permutes with every Sylow subgroup of BI H is called weakly s-supplemented in G if there is a subgroup T of G such that G = HT and H a (c) T a parts per thousand currency signaEuro parts per thousand H (sG) ; where H (sG) is the subgroup of H generated by all subgroups of H that are s-quasinormal in G: We investigate the influence of ss-quasinormal and weakly s-supplemented subgroups on the structure of finite groups. Some recent results are generalized and unified.