On the composition factors of a group with the same prime graph as $B_{n}(5)$

Title:

On the composition factors of a group with the same prime graph as $B_{n}(5)$

Creator:

Babai, Azam and Khosravi, Behrooz

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:7cd46288-3471-4ed6-93cc-d2f6fbf7136d
uuid:7cd46288-3471-4ed6-93cc-d2f6fbf7136d

Subject:

prime graph, simple group, recognition, and quasirecognition

Type:

model:article and TEXT

Format:

bez média and svazek

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 $C_{n}(5)$.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

469-486

Source:

Czechoslovak Mathematical Journal | 2012 Volume:62 | Number:2

Harvested from:

CDK

Metadata only:

false