Article
| Title: | Some results on Sylow numbers of finite groups (English) |
| Author: | Liu, Yang |
| Author: | Zhang, Jinjie |
| Language: | English |
| Journal: | Czechoslovak Mathematical Journal |
| ISSN: | 0011-4642 (print) |
| ISSN: | 1572-9141 (online) |
| Volume: | 74 |
| Issue: | 4 |
| Year: | 2024 |
| Pages: | 1083-1095 |
| Summary lang: | English |
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| Category: | math |
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| Summary: | We study the group structure in terms of the number of Sylow $p$-subgroups, which is denoted by $n_p(G)$. The first part is on the group structure of finite group $G$ such that $n_p(G)=n_p(G/N)$, where $N$ is a normal subgroup of $G$. The second part is on the average Sylow number ${\rm asn}(G)$ and we prove that if $G$ is a finite nonsolvable group with ${\rm asn}(G)<39/4$ and ${\rm asn}(G)\neq 29/4$, then $G/F(G)\cong A_5$, where $F(G)$ is the Fitting subgroup of $G$. In the third part, we study the nonsolvable group with small sum of Sylow numbers. (English) |
| Keyword: | Sylow number |
| Keyword: | nonsolvable group |
| MSC: | 20D05 |
| MSC: | 20D20 |
| DOI: | 10.21136/CMJ.2024.0466-23 |
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| Date available: | 2024-12-15T06:36:02Z |
| Last updated: | 2024-12-16 |
| Stable URL: | http://hdl.handle.net/10338.dmlcz/152690 |
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