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2022•Communications in AlgebraRequires access

On weakly H-subgroups of finite groups II*

Ruifang Chen, Xiaoli Li, Xianhe Zhao

Open publisher page 7 citations

Abstract

Let G be a group. A subgroup H of G is called an H-subgroup in G if NG(H)∩Hx≤H for all x∈G. Furthermore, a subgroup H of G is called a weakly H-subgroup in G if there exists a normal subgroup K of G such that G = HK and H∩K is an H-subgroup in G. In this article, some new criteria for a group to be p-nilpotent and supersolvable are given.

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What this paper is about

Let G be a group. A subgroup H of G is called an H-subgroup in G if NG(H)∩Hx≤H for all x∈G. Furthermore, a subgroup H of G is called a weakly H-subgroup in G if there exists a normal subgroup K of G such that G = HK and H∩K is an H-subgroup in G. In this article, some new criteria for a group to be p-nilpotent and supersolvable are given.

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OpenAlex reports 7 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

Let G be a group. A subgroup H of G is called an H-subgroup in G if NG(H)∩Hx≤H for all x∈G. Furthermore, a subgroup H of G is called a weakly H-subgroup in G if there exists a normal subgroup K of G such that G = HK and H∩K is an H-subgroup in G. In this article, some new criteria for a group to be p-nilpotent and supersolvable are given.

Key concepts: Mathematics, Index of a subgroup, Subgroup, Characteristic subgroup, Normal subgroup, Maximal subgroup, Fitting subgroup, Combinatorics

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