Let G be a finite group and H a subgroup of G.We say that H is S-permutable in G if H permutes with every Sylow subgroup of G.A group G is called a generalized smooth group(GS-group)if[G/L]is totally smooth for every ...Let G be a finite group and H a subgroup of G.We say that H is S-permutable in G if H permutes with every Sylow subgroup of G.A group G is called a generalized smooth group(GS-group)if[G/L]is totally smooth for every subgroup L of G of prime order.In this paper,we investigate the structure of G under the assumption that each subgroup of prime order is S-permutable if the maximal subgroups of G are GS-groups.展开更多
文摘Let G be a finite group and H a subgroup of G.We say that H is S-permutable in G if H permutes with every Sylow subgroup of G.A group G is called a generalized smooth group(GS-group)if[G/L]is totally smooth for every subgroup L of G of prime order.In this paper,we investigate the structure of G under the assumption that each subgroup of prime order is S-permutable if the maximal subgroups of G are GS-groups.
