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2021•Communications in AlgebraRequires access

Finite groups with S-quasinormal subgroups

Wei Meng, Yan Deng, Jiakuan Lu

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Abstract

Let G be a finite group. A minimal subgroup of G is a subgroup of prime order. A subgroup of G is called S-quasinormal in G if it permutes with each Sylow subgroup of G. A group G is called an MS-group if each minimal subgroup of G is S-quasinormal in G. In this paper, we study the structure of finite groups all of whose maximal subgroups of even order are MS-groups. Furthermore, we determine the finite non-abelian simple groups all of whose second maximal subgroups of even order are MS-groups.

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What this paper is about

Let G be a finite group. A minimal subgroup of G is a subgroup of prime order. A subgroup of G is called S-quasinormal in G if it permutes with each Sylow subgroup of G. A group G is called an MS-group if each minimal subgroup of G is S-quasinormal in G. In this paper, we study the structure of finite groups all of whose maximal subgroups of even order are MS-groups. Furthermore, we determine the finite non-abelian simple groups all of whose second maximal subgroups of even order are MS-groups.

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Available abstract

Let G be a finite group. A minimal subgroup of G is a subgroup of prime order. A subgroup of G is called S-quasinormal in G if it permutes with each Sylow subgroup of G. A group G is called an MS-group if each minimal subgroup of G is S-quasinormal in G. In this paper, we study the structure of finite groups all of whose maximal subgroups of even order are MS-groups. Furthermore, we determine the finite non-abelian simple groups all of whose second maximal subgroups of even order are MS-groups.

Key concepts: Mathematics, Sylow theorems, Index of a subgroup, p-group, Omega and agemo subgroup, Locally finite group, Fitting subgroup, Finite group

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