1. On the composition factors of a group with the same prime graph as $B_{n}(5)$
- Creator:
- Babai, Azam and Khosravi, Behrooz
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- prime graph, simple group, recognition, and quasirecognition
- Language:
- English
- Description:
- 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 $C_{n}(5)$.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public