On S-c-propermutable subgroups of finite groups

A subgroup H of a group G is said to be S-c-propermutable in G if G has a subgroup B such that G=N_G(H)B and for every Sylow subgroup A of B, there exists an element x∈B such that HA^x=A^xH. Here, S-c-propermutable subgroups were used to study the structure of finite groups and some new criteria of supersoluble groups were obtained.