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Journal of Applied Mathematics and Computation

ISSN Print: 2576-0645 Downloads: 145441 Total View: 1795428
Frequency: quarterly ISSN Online: 2576-0653 CODEN: JAMCEZ
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Article Open Access http://dx.doi.org/10.26855/jamc.2022.12.016

The Influence of m-σ-embedded Subgroups on the Structure of Finite Groups

Songnian Xu, Chi Zhang*

Department of Mathematics, China University of Mining and Technology, Xuzhou 221116, Jiangsu, China.

*Corresponding author: Chi Zhang

Published: January 14,2023

Abstract

Let σ={σi│i∈I} be some partition of the set of all primes P and G is a finite group. A group is said to be σ-primary if it is a finite σi-group for some i. A subgroup A of G is said to be σ-subnormal in G if there is a subgroup chain A= A0≤A1≤• • •≤At=G such that either A(i-1)⊴Ai or Ai/〖(A(i-1))〗(Ai ) is σ-primary for all i=1,⋯,t. A subgroupS of G is m-σ-permutable in G if S=〈M,B〉 for some modular subgroup M and σ-permutable subgroup B of G. Following this, a subgroup H of G is m-σ-embedded in G if there exist an m-σ-permutable subgroup S and a σ-subnormal subgroup T of Gsuch that HG = HT and H∩T≤S≤H, where HG=⟨Hx│x∈G⟩ is the normal closure of H in G. In this paper, we study the structure of G under the condition that some given subgroups of G are m-σ-embedded in G. Some available results are generalized.

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How to cite this paper

The Influence of m-σ-embedded Subgroups on the Structure of Finite Groups

How to cite this paper:  Songnian Xu, Chi Zhang. (2022) The Influence of m-σ-embedded Subgroups on the Structure of Finite Groups. Journal of Applied Mathematics and Computation6(4), 523-528.

DOI: http://dx.doi.org/10.26855/jamc.2022.12.016