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.

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

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
Mots-clés : prime graph; simple group; recognition; quasirecognition 
@article{10_1007_s10587_012_0022_9,
     author = {Babai, Azam and Khosravi, Behrooz},
     title = {On the composition factors of a group with the same prime graph as $B_{n}(5)$},
     journal = {Czechoslovak Mathematical Journal},
     pages = {469--486},
     publisher = {mathdoc},
     volume = {62},
     number = {2},
     year = {2012},
     doi = {10.1007/s10587-012-0022-9},
     mrnumber = {2990187},
     zbl = {1249.20014},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-012-0022-9/}
}
TY  - JOUR
AU  - Babai, Azam
AU  - Khosravi, Behrooz
TI  - On the composition factors of a group with the same prime graph as $B_{n}(5)$
JO  - Czechoslovak Mathematical Journal
PY  - 2012
SP  - 469
EP  - 486
VL  - 62
IS  - 2
PB  - mathdoc
UR  - https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-012-0022-9/
DO  - 10.1007/s10587-012-0022-9
LA  - en
ID  - 10_1007_s10587_012_0022_9
ER  - 
%0 Journal Article
%A Babai, Azam
%A Khosravi, Behrooz
%T On the composition factors of a group with the same prime graph as $B_{n}(5)$
%J Czechoslovak Mathematical Journal
%D 2012
%P 469-486
%V 62
%N 2
%I mathdoc
%U https://geodesic-test.mathdoc.fr/articles/10.1007/s10587-012-0022-9/
%R 10.1007/s10587-012-0022-9
%G en
%F 10_1007_s10587_012_0022_9
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/

Cité par Sources :