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

Babai, Azam; Khosravi, Behrooz

doi:10.1007/s10587-012-0022-9

Geodesic

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On the composition factors of a group with the same prime graph as

B_{n} (5)

Babai, Azam ; Khosravi, Behrooz

Czechoslovak Mathematical Journal, Tome 62 (2012) no. 2, pp. 469-486.

Voir la notice de l'article dans Czech Digital Mathematics Library

Résumé

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

p q

. The prime graph of

G

is denoted by

Γ (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

Γ (G) = Γ (B_{n} (5))

, where

n \geq 6

, then

G

has a unique nonabelian composition factor isomorphic to

B_{n} (5)

C_{n} (5)

MR Zbl

DOI : 10.1007/s10587-012-0022-9

Classification : 05C25, 20D05, 20D06, 20D60
Mots-clés : prime graph; simple group; recognition; quasirecognition

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     title = {On the composition factors of a group with the same prime graph as $B_{n}(5)$},
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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. https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-012-0022-9/

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