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2013•Journal of Algebra and Its ApplicationsRequires access

FINITE GROUPS ALL OF WHOSE MAXIMAL SUBGROUPS OF EVEN ORDER ARE ℋp-GROUPS

Wei Meng, Jiakuan Lu

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Abstract

Let G be a finite group. A subgroup H of G is called an ℋ-subgroup of G if NG(H) ∩ Hg ≤ H for all g ∈ G; G is said to be an ℋp-group if every cyclic subgroup of G of prime order or order 4 is an ℋ-subgroup of G. In this paper, the structure of the finite groups all of whose maximal subgroups of even order are ℋp-subgroups have been characterized.

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What this paper is about

Let G be a finite group. A subgroup H of G is called an ℋ-subgroup of G if NG(H) ∩ Hg ≤ H for all g ∈ G; G is said to be an ℋp-group if every cyclic subgroup of G of prime order or order 4 is an ℋ-subgroup of G. In this paper, the structure of the finite groups all of whose maximal subgroups of even order are ℋp-subgroups have been characterized.

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Available abstract

Let G be a finite group. A subgroup H of G is called an ℋ-subgroup of G if NG(H) ∩ Hg ≤ H for all g ∈ G; G is said to be an ℋp-group if every cyclic subgroup of G of prime order or order 4 is an ℋ-subgroup of G. In this paper, the structure of the finite groups all of whose maximal subgroups of even order are ℋp-subgroups have been characterized.

Key concepts: Mathematics, Index of a subgroup, Subgroup, Maximal subgroup, Characteristic subgroup, Order (exchange), p-group, Combinatorics

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