Characterization of $mathrm{PSL} (5,q) by its Order and One Conjugacy Class Size

Author(s):

A.R. Khalili Asboei*

Message:
Article Type:
Research/Original Article (دارای رتبه معتبر)
Abstract:

Let $p=(q^4+q^3+q^2+q+1)/(5,q-1)$ be a prime number, where $q$ is a prime power. In this paper, we will show $Gcong mathrm{PSL}(5,q)$ if and only if $|G|=|mathrm{PSL}(5,q)|$, and $G$ has a conjugacy class size $frac{| mathrm{PSL}(5,q)|}{p}$. Further, the validity of a conjecture of J. G. Thompson is generalized to the groups under consideration by a new way. the formula is not displayed correctly!

Keywords:

Conjugacy class size , Prime graph , Thompson's conjecture

Language:
English
Published:
Iranian Journal of Mathematical Sciences and Informatics, Volume:15 Issue: 1, May 2020
Pages:
35 to 40
https://www.magiran.com/p2127008  
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