Sajjadi, M., Bibak, M., Rezaeezadeh, G. (2016). Characterization of some projective special linear groups in dimension four by their orders and degree patterns. Bulletin of the Iranian Mathematical Society, 42(1), 27-36.
M. Sajjadi; M. Bibak; G. R. Rezaeezadeh. "Characterization of some projective special linear groups in dimension four by their orders and degree patterns". Bulletin of the Iranian Mathematical Society, 42, 1, 2016, 27-36.
Sajjadi, M., Bibak, M., Rezaeezadeh, G. (2016). 'Characterization of some projective special linear groups in dimension four by their orders and degree patterns', Bulletin of the Iranian Mathematical Society, 42(1), pp. 27-36.
Sajjadi, M., Bibak, M., Rezaeezadeh, G. Characterization of some projective special linear groups in dimension four by their orders and degree patterns. Bulletin of the Iranian Mathematical Society, 2016; 42(1): 27-36.
Characterization of some projective special linear groups in dimension four by their orders and degree patterns
Receive Date: 05 April 2014,
Revise Date: 10 October 2014,
Accept Date: 10 October 2014
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 $G\cong L_{4}(2^{n})$.
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