Characterizations of finite groups with σ-semiembedded subgroups
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Published:2022-05-31
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Volume:
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ISSN:0219-4988
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Container-title:Journal of Algebra and Its Applications
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language:en
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Short-container-title:J. Algebra Appl.
Author:
Cao Chenchen1,
Guo Wenbin2ORCID
Affiliation:
1. School of Mathematics and Statistics, Ningbo University, Ningbo 315211, P. R. China
2. School of Science, Hainan University, Haikou 570225, P. R. China
Abstract
Let [Formula: see text] be a partition of the set of all primes [Formula: see text], [Formula: see text] a finite group and [Formula: see text]. A set [Formula: see text] of subgroups of [Formula: see text] is said to be a complete Hall[Formula: see text]-set of [Formula: see text] if every non-identity member of [Formula: see text] is a Hall [Formula: see text]-subgroup of [Formula: see text] for some [Formula: see text] and [Formula: see text] contains exactly one Hall [Formula: see text]-subgroup of [Formula: see text] for every [Formula: see text]. A subgroup [Formula: see text] of [Formula: see text] is said to be: [Formula: see text]-permutable in [Formula: see text] if [Formula: see text] has a complete Hall [Formula: see text]-set [Formula: see text] such that [Formula: see text] for all [Formula: see text] and all [Formula: see text]; [Formula: see text]-semipermutable in [Formula: see text] if [Formula: see text] has a complete Hall [Formula: see text]-set [Formula: see text] such that [Formula: see text] for all [Formula: see text] and all [Formula: see text]-group [Formula: see text] with [Formula: see text]. We say that [Formula: see text] is [Formula: see text]-semiembedded in [Formula: see text] if there exists a [Formula: see text]-permutable subgroup [Formula: see text] of [Formula: see text] such that [Formula: see text] is a [Formula: see text]-permutable subgroup of [Formula: see text] and [Formula: see text], where [Formula: see text] denotes the subgroup of [Formula: see text] which is generated by all [Formula: see text]-semipermutable subgroups of [Formula: see text] contained in [Formula: see text]. In this paper, we study the influence of [Formula: see text]-semiembedded subgroups on the structure of finite groups. Some known results are generalized and unified.
Funder
National Natural Science Foundation of China
Natural Science Foundation of Jilin Province
Publisher
World Scientific Pub Co Pte Ltd
Subject
Applied Mathematics,Algebra and Number Theory