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Recognition of the group $G_2(5)$ by the prime graph | ||
Journal of Linear and Topological Algebra | ||
مقاله 8، دوره 01، شماره 02، شهریور 2012، صفحه 115-120 اصل مقاله (118.01 K) | ||
نویسندگان | ||
P. Nosratpour* 1؛ M. R. Darafsheh2 | ||
1Department of mathematics, ILam Branch, Islamic Azad university, Ilam, Iran | ||
2School of Mathematics, statistics and Computer Science, College of Science, University of Tehran, Tehran, Iran | ||
چکیده | ||
Let $G$ be a finite group. The prime graph of $G$ is a graph $\Gamma(G)$ with vertex set $\pi(G)$, the set of all prime divisors of $|G|$, and two distinct vertices $p$ and $q$ are adjacent by an edge if $G$ has an element of order $pq$. In this paper we prove that if $\Gamma(G)=\Gamma(G_2(5))$, then $G$ has a normal subgroup $N$ such that $\pi(N)\subseteq\{2,3,5\}$ and $G/N\equiv G_2(5)$. | ||
کلیدواژهها | ||
prime graph؛ recognition؛ linear group | ||
مراجع | ||
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