On the average number of Sylow subgroups in finite groups

Khalili Asboei, Alireza, and Salehi Amiri, Seyed Sadegh. "On the average number of Sylow subgroups in finite groups." Czechoslovak Mathematical Journal 72.3 (2022): 747-750. <http://eudml.org/doc/298372>.

@article{KhaliliAsboei2022,
abstract = {We prove that if the average number of Sylow subgroups of a finite group is less than $\tfrac\{41\}\{5\}$ and not equal to $\tfrac\{29\}\{4\}$, then $G$ is solvable or $G/F(G)\cong A_\{5\}$. In particular, if the average number of Sylow subgroups of a finite group is $\tfrac\{29\}\{4\}$, then $G/N\cong A_\{5\}$, where $N$ is the largest normal solvable subgroup of $G$. This generalizes an earlier result by Moretó et al.},
author = {Khalili Asboei, Alireza, Salehi Amiri, Seyed Sadegh},
journal = {Czechoslovak Mathematical Journal},
keywords = {Sylow number; non-solvable group},
language = {eng},
number = {3},
pages = {747-750},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the average number of Sylow subgroups in finite groups},
url = {http://eudml.org/doc/298372},
volume = {72},
year = {2022},
}

TY - JOUR
AU - Khalili Asboei, Alireza
AU - Salehi Amiri, Seyed Sadegh
TI - On the average number of Sylow subgroups in finite groups
JO - Czechoslovak Mathematical Journal
PY - 2022
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 72
IS - 3
SP - 747
EP - 750
AB - We prove that if the average number of Sylow subgroups of a finite group is less than $\tfrac{41}{5}$ and not equal to $\tfrac{29}{4}$, then $G$ is solvable or $G/F(G)\cong A_{5}$. In particular, if the average number of Sylow subgroups of a finite group is $\tfrac{29}{4}$, then $G/N\cong A_{5}$, where $N$ is the largest normal solvable subgroup of $G$. This generalizes an earlier result by Moretó et al.
LA - eng
KW - Sylow number; non-solvable group
UR - http://eudml.org/doc/298372
ER -