TY - JOUR
T1 - Characterization of $mathrm{PSL}(5,q)$ by its Order and One Conjugacy Class Size
TT -
JF - IJMSI
JO - IJMSI
VL - 15
IS - 1
UR - http://ijmsi.ir/article-1-1061-en.html
Y1 - 2020
SP - 35
EP - 40
KW - Conjugacy class size
KW - Prime graph
KW - Thompson's conjecture.
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.
M3 10.29252/ijmsi.15.1.35
ER -