TY - JOUR JF - IJMSI JO - IJMSI VL - 15 IS - 1 PY - 2020 Y1 - 2020/4/01 TI - Characterization of $mathrm{PSL}(5,q)$ by its Order and One Conjugacy Class Size TT - N2 - 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. SP - 35 EP - 40 AU - Khalili Asboei, A.R. AD - Department of Mathematics, Farhangian University KW - Conjugacy class size KW - Prime graph KW - Thompson's conjecture. UR - http://ijmsi.ir/article-1-1061-en.html DO - 10.29252/ijmsi.15.1.35 ER -