Geodesic
Some results on Sylow numbers of finite groups
Czechoslovak Mathematical Journal, Tome 74 (2024) no. 4, pp. 1083-1095
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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.
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.
DOI : 10.21136/CMJ.2024.0466-23
Classification : 20D05, 20D20
Keywords: Sylow number; nonsolvable group 
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Liu, Yang; Zhang, Jinjie. Some results on Sylow numbers of finite groups. Czechoslovak Mathematical Journal, Tome 74 (2024) no. 4, pp. 1083-1095. doi: 10.21136/CMJ.2024.0466-23

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