Geodesic
On the composition factors of a group with the same prime graph as $B_{n}(5)$
Czechoslovak Mathematical Journal, Tome 62 (2012) no. 2, pp. 469-486

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Let $G$ be a finite group. The prime graph of $G$ is a graph whose vertex set is the set of prime divisors of $|G|$ and two distinct primes $p$ and $q$ are joined by an edge, whenever $G$ contains an element of order $pq$. The prime graph of $G$ is denoted by $\Gamma (G)$. It is proved that some finite groups are uniquely determined by their prime graph. In this paper, we show that if $G$ is a finite group such that $\Gamma (G)=\Gamma (B_{n}(5))$, where $n\geq 6$, then $G$ has a unique nonabelian composition factor isomorphic to $B_{n}(5)$ or $C_{n}(5)$.
DOI : 10.1007/s10587-012-0022-9
Classification : 05C25, 20D05, 20D06, 20D60
Keywords: prime graph; simple group; recognition; quasirecognition 
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Babai, Azam; Khosravi, Behrooz. On the composition factors of a group with the same prime graph as $B_{n}(5)$. Czechoslovak Mathematical Journal, Tome 62 (2012) no. 2, pp. 469-486. doi: 10.1007/s10587-012-0022-9

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