On the composition factors of a group with the same prime graph as B n (5)

Abstract

On the composition factors of a group with the same prime graph as B n (5) Czechoslovak Mathematical Journal, Vol. 62 (2012) Abstract. 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 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(Bn (5)), where n 6, then G has a unique nonabelian composition factor isomorphic to Bn(5) or Cn(5).

Квазираспознаваемость $^2D_{n}(3^\alpha)$ по графу простых чисел при $n=4m+1\ge 21$ и нечетном $\alpha$

“…В [7]- [9] определяются конечные группы с таким же графом простых чисел, как у PSL(2, ), где не является простым числом, и как у (3), где простое. А в работе [10] доказано, что если Γ( ) = Γ( (5)) при > 6, то имеет единственный неабелев композиционный фактор, изоморфный (5) или (5). Доказано, что простая группа 4 ( ), где = 2 > 2 (см.…”

Quasirecognition by prime graph of $C_{n}(4) $, where $ n\geq17 $ is odd

“…A finite non-abelian simple group G is quasirecognizable by its prime graph, if each finite group P with Γ(P ) = Γ(G) has a unique non-abelian composition factor isomorphic to G [5]. The most recent lists of finite simple groups that are quasirecognizable by prime graph are presented in [2], [4], [6], [7] and [8].…”

On recognition by prime graph of the projective special linear group over GF(3)

“…In [20,21,22,24,27,28] finite groups with the same prime graph as PSL n (2), U n (2), D n (2), B n (3) and 2 D n (2) are obtained. In [3,4], it is proved that 2 D 2 m +1 (3) is recognizable by prime graph.…”