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Let $\textit{G}$ be a finite group. We construct the prime graph
of $\textit{G}$ as follows: the vertices of this graph are the
prime divisors of $|\textit{G}|$ and two vertices $\textit{p}$ and
$\textit{q}$ are joined by and edge if and only if $\textit{G}$
contains an element of order $\textit{pq}$. The prime graph of
$\textit{G}$ is the denoted by $\Gamma(G)$.\\ Mina Hagie (Comm.
Algebra, 2003) determined finite groups $\textit{G}$ such that
$\Gamma(G)=\Gamma(S)$, where $\textit{S}$ is a sporadic simple
group. In this paper we determine finite groups $\textit{G}$ such
that $\Gamma(G)=\Gamma(L_{2}(q))$ for some $\textit{q}<100$.
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