Semipermutable subgroups and s-semipermutable subgroups in finite groups

doi:10.1007/s11464-022-1002-5

Front. Math. China

2022, Vol. 17

Issue (1) : 23-46 https://doi.org/10.1007/s11464-022-1002-5

SURVEY ARTICLE

Semipermutable subgroups and s-semipermutable subgroups in finite groups

Yangming LI(

)

School of Mathematics, Guangdong University of Education, Guangzhou 510310, China

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Abstract

Suppose that H is a subgroup of a finite group G. We call H is semipermutable in G if HK = KH for any subgroup K of G such that (|H|, |K|) = 1; H is s-semipermutable in G if HG_p = G_pH, for any Sylow p-subgroup G_p of G such that (|H|, p) = 1. These two concepts have been received the attention of many scholars in group theory since they were introduced by Professor Zhongmu Chen in 1987. In recent decades, there are a lot of papers published via the application of these concepts. Here we summarize the results in this area and gives some thoughts in the research process.

Keywords Semipermutable subgroup s-semipermutable subgroup maximal subgroup minimal subgroup the generalized Fitting-subgroup formation

Corresponding Author(s): Yangming LI

Issue Date: 19 May 2022

Cite this article:

Yangming LI. Semipermutable subgroups and s-semipermutable subgroups in finite groups[J]. Front. Math. China, 2022, 17(1): 23-46.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-022-1002-5
https://academic.hep.com.cn/fmc/EN/Y2022/V17/I1/23

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