Recognition of the groups $L_5(4)$ and $U_4(4)$ by the prime graph

  • M. R. Darafsheh
  • P. Nosratpour

Abstract

Let $G$ be a finite group. The prime graph of $G$ is the graph $\Gamma(G)$ whose vertex set is the set $\Pi(G)$ of all prime divisors of the order $|G|$ and two distinct vertices $p$ and $q$ of which are adjacent by an edge if $G$ has an element of order $pq$. We prove that if $S$ denotes one of the simple groups $L_5(4)$ and $U_4(4)$ and if $G$ is a finite group with $\Gamma(G) = \Gamma(S)$, then $G$ has a $G$ normal subgroup $N$ such that $\Pi(N) \subseteq \{2, 3, 5\}$ and $\cfrac GN \cong S$.
Published
25.02.2012
How to Cite
DarafshehM. R., and NosratpourP. “Recognition of the Groups $L_5(4)$ and $U_4(4)$ by the Prime Graph”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, no. 2, Feb. 2012, pp. 210-7, http://umj.imath.kiev.ua/index.php/umj/article/view/2567.
Section
Research articles