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Khalili Asboei A. Characterization of $mathrm{PSL}(5,q)$ by its Order and One Conjugacy Class Size. IJMSI. 2020; 15 (1) :35-40

URL: http://ijmsi.ir/article-1-1061-en.html

URL: http://ijmsi.ir/article-1-1061-en.html

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.

Type of Study: Research paper |
Subject:
Special

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