The prime graph $\Gamma(G)$ of a group $G$ is
a graph with vertex set $\pi(G)$, the set of primes dividing the
order of $G$, and two distinct vertices $p$ and $q$ are adjacent
by an edge written $p\sim q$ if there is an element in $G$ of
order $pq$. Let $\pi(G)=\{p_{1},p_{2},...,p_{k}\}$. For
$p\in\pi(G)$, set $deg(p):=|\{q \in\pi(G)| p\sim q\}|$, which is
called the degree of $p$. We also set
$D(G):=(deg(p_{1}),deg(p_{2}),...,deg(p_{k}))$, where
$p_{1}<p_{2}<...<p_{k}$, which is called degree pattern of $G$.
The group $G$ is called $k$-fold OD-characterizable if there exists
exactly $k$ non-isomorphic groups $M$ satisfying conditions
$|G|=|M|$ and $D(G)=D(M)$. In particular, a $1$-fold
OD-characterizable group is simply called OD-characterizable. In
this paper, as the main result, we prove that projective special
linear group $L_{3}(2^{n})$ where $n\in\{4,5,6,7,8,10,12\}$ is
OD-characterizable.
Rezaeezadeh, G. R., Bibak, M., & Sajjadi, M. (2015). Characterization of projective special linear groups in dimension three by their orders and degree patterns. Bulletin of the Iranian Mathematical Society, 41(3), 551-580.
MLA
G. R. Rezaeezadeh; M. Bibak; M. Sajjadi. "Characterization of projective special linear groups in dimension three by their orders and degree patterns". Bulletin of the Iranian Mathematical Society, 41, 3, 2015, 551-580.
HARVARD
Rezaeezadeh, G. R., Bibak, M., Sajjadi, M. (2015). 'Characterization of projective special linear groups in dimension three by their orders and degree patterns', Bulletin of the Iranian Mathematical Society, 41(3), pp. 551-580.
VANCOUVER
Rezaeezadeh, G. R., Bibak, M., Sajjadi, M. Characterization of projective special linear groups in dimension three by their orders and degree patterns. Bulletin of the Iranian Mathematical Society, 2015; 41(3): 551-580.