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
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
Journal title :
Bulletin of the Iranian Mathematical Society