ON m-sigma-EMBEDDED SUBGROUPS OF FINITE GROUPS
ON m-sigma-EMBEDDED SUBGROUPS OF FINITE GROUPS
复制标题
有限群的 m-sigma 嵌入子群
DOI：
10.1007/s10474-021-01176-0
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发表时间：
2021
影响因子：
0.9
通讯作者：
Zhang C.
中科院分区：
文献类型：
--
作者：
Guo J.;Guo W.;Qiao S.;Zhang C.
设是素数集合的某个划分，G是有限群。 一个群称为-素群，如果它是有限群。G的子群A称为G中的-次正规子群，如果存在子群链使得对所有子群都是-素子群。对于某个模子群Mand-可置换子群BofG，给出了一个子群SofGism--permutableinGif.我们称G的子群Hofism--嵌入G中，如果存在G的m--置换子群和a--次正规子群T，使得和，这里是HinG的正规闭包.本文研究了m--嵌入子群的性质，并利用它们来确定有限群的结构.推广了已有的结果。
Letbe some partition of the set of all primesandGbe a finite group. A group is said to be-primaryif it is a finite-group for somei. A subgroupAofGis said to be-subnormalinGif there is a subgroup chainsuch that eitheroris-primary for all. A subgroupSofGism--permutableinGiffor some modular subgroupMand-permutable subgroupBofG. We say that a subgroupHofGism--embedded in Gif there exist anm--permutable subgroupSand a-subnormal subgroupTofGsuch thatand, whereis the normal closure ofHinG.In this paper, we study the properties ofm--embedded subgroups and use them to determine the structure of finite groups. Some known results are generalized.