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Finite Groups with Certain S-Permutable and GS-Maximal Subgroups
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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.
Title: Finite Groups with Certain S-Permutable and GS-Maximal Subgroups
Description:
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.
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