Some results on Sylow numbers of finite groups

Liu, Yang, and Zhang, Jinjie. "Some results on Sylow numbers of finite groups." Czechoslovak Mathematical Journal 74.4 (2024): 1083-1095. <http://eudml.org/doc/299647>.

@article{Liu2024,
abstract = {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 $\{\rm asn\}(G)\ne 29/4$, 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.},
author = {Liu, Yang, Zhang, Jinjie},
journal = {Czechoslovak Mathematical Journal},
keywords = {Sylow number; nonsolvable group},
language = {eng},
number = {4},
pages = {1083-1095},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some results on Sylow numbers of finite groups},
url = {http://eudml.org/doc/299647},
volume = {74},
year = {2024},
}

TY - JOUR
AU - Liu, Yang
AU - Zhang, Jinjie
TI - Some results on Sylow numbers of finite groups
JO - Czechoslovak Mathematical Journal
PY - 2024
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 74
IS - 4
SP - 1083
EP - 1095
AB - 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 ${\rm asn}(G)\ne 29/4$, 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.
LA - eng
KW - Sylow number; nonsolvable group
UR - http://eudml.org/doc/299647
ER -