Author/Authors :
Sajjadi ، Masoumeh نويسنده Payame Noor University , , Bibak، Masoumeh نويسنده University of Shahrekord ,
Abstract :
Let $G$ be a finite group. The degree pattern of $G$ denoted by
$D(G)$ is defined as follows: If $\pi(G)=\{p_{1},p_{2},...,p_{k}\}$ such that
$p_{1} < p_{2} < ... < p_{k}$, then $D(G):=(deg(p_{1}),deg(p_{2}),...,deg(p_{k}))$, where $deg(p_{i})$
for $1\leq i\leq k$, are the degree of vertices $p_{i}$ in the
prime graph of $G$. In this article < , > we consider a finite group $G$
under assumptions $|G|=|L_{4}(2^{n})|$ and $D(G)=D(L_{4}(2^{n}))$,
where $n\in\{5, 6, 7\}$ and we prove that $G\cong L_{4}(2^{n})$.
