On the prime graph of <i>D_n</i>(<i>q</i>) where <i>q</i> ∈ {2; 5}

Abstract

Let G be a nite group. The prime graph Γ(G) of G is de ned as follows. The vertices of Γ(G) are the primes dividing the order of G and two distinct vertices p, p′ are joined by an edge if G has an element of order pp′. Let L = D_n(q) have disconnected prime graph and q ∈ {2; 5}. In this paper, we determine nite groups G with the same prime graph as L, i.e. Γ(G) = Γ(L).

Keywords: Prime graph, simple group, recognition, quasirecognition

Quaestiones Mathematicae 36(2013), 517-535