Title of article :
OD-Characterization of almost simple groups related to $L_{3}(25)$
Author/Authors :
Darafsheh، Mohamamad Reza نويسنده ‎University‎ ‎of Tehran‎ , , Rezaeezadeh، Gholam Reza نويسنده University‎ ‎of Shahrekord‎ , , Sajjadi، M. نويسنده niversity‎ ‎of Shahrekord‎ , , Bibak، Masoumeh نويسنده University‎ ‎of Shahrekord‎ ,
Issue Information :
دوماهنامه با شماره پیاپی سال 2014
Pages :
26
From page :
765
To page :
790
Abstract :
Let $G$ be a finite group and $\pi(G)$ be the set of all the prime‎ ‎divisors of $|G|$‎. ‎The prime graph of $G$ is a simple graph‎ ‎$\Gamma(G)$ whose vertex set is $\pi(G)$ and two distinct vertices‎ ‎$p$ and $q$ are joined by an edge if and only if $G$ has an‎ ‎element of order $pq$‎, ‎and in this case we will write $p\sim q$‎. ‎The degree of $p$ is the number of vertices adjacent to $p$ and is‎ ‎denoted by $deg(p)$‎. ‎If‎ ‎$|G|=p^{\alpha_{1}}_{1}p^{\alpha_{2}}_{2}...p^{\alpha_{k}}_{k}$‎, ‎$p_{i}^{,}$s different primes‎, ‎$p_{1} < p_{2} < ... < p_{k}$‎, ‎then‎ ‎$D(G)=(deg(p_{1}),deg(p_{2}),...,deg(p_{k}))$ is called the degree‎ ‎pattern of $G$‎. ‎A finite group $G$ is called $k$-fold‎ ‎OD-characterizable if there exist exactly $k$ non-isomorphic‎ ‎groups $S$ with $|G|=|S|$ and $D(G)=D(S)$‎. ‎In this paper‎, ‎we‎ ‎characterize groups with the same order and degree‎ ‎pattern as an almost simple groups related to $L_{3}(25)$‎.
Journal title :
Bulletin of the Iranian Mathematical Society
Serial Year :
2014
Journal title :
Bulletin of the Iranian Mathematical Society
Record number :
1339065
Link To Document :
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