2017
Том 69
№ 9

All Issues

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

Darafsheh M. R., Nosratpour P.

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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 $\cfrac GN \cong S$.

English version (Springer): Ukrainian Mathematical Journal 64 (2012), no. 2, pp 238-246.

Citation Example: Darafsheh M. R., Nosratpour P. Recognition of the groups $L_5(4)$ and $U_4(4)$ by the prime graph // Ukr. Mat. Zh. - 2012. - 64, № 2. - pp. 210-217.

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