Article
| Title: | On conditionally permutable subgroups and supersolubility (English) |
| Author: | Zhang, Yifan |
| Author: | Yu, Mengxue |
| Author: | Li, Baojun |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 76 |
| Issue: | 3 |
| Year: | 2026 |
| Pages: | 927-934 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | Let $H$, $K$ be subgroups of $G$. Then $H$ and $K$ are called c-permutable in $G$ if there exists an element $x\in G$ such that $HK^x = K^xH$. By imposing c-permutability conditions on the members of a maximal subgroup series of $G$, we give some new criteria for the supersolubility of a finite group. We prove that if $G$ is a soluble group with a maximal subgroup series $1=M_0< M_1<\cdots < M_{s-1}< M_s=G$, where $M_i$ is c-permutable in $G$ for every $i=0,1,\cdots ,s$, then $G$ is supersoluble. On this basis, if $G$ is not soluble, but we have the condition that $M_i$ is c-permutable in $M_{i+1}$ $(0\leq i\leq s-1)$, then $G$ is also supersoluble. These results provide new characterizations of supersoluble groups. (English) |
| Keyword: | finite group |
| Keyword: | supersolublilty |
| Keyword: | c-permutable subgroup |
| Keyword: | maximal subgroup series |
| MSC: | 20D10 |
| MSC: | 20D25 |
| DOI: | 10.21136/CMJ.2026.0451-25 |
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| Date available: | 2026-09-11T13:14:43Z |
| Last updated: | 2026-09-14 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/153735 |
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