On the prime graph of Dn(q) where q ∊ {2, 5}

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