Quasirecognition by prime graph of simple group Dn(3)

Abstract

Let G be a finite group. The prime graph (G) of G is defined as follows. The vertices of (G) are the primes dividing the order of G and two distinct vertices p and p′ are joined by an edge if there is an element in G of order pp′. It is proved that Dn(q), with disconnected prime graph, is quasirecognizable by their element orders. In this paper as the main result, we show that Dn(3), where n € {p,p+ 1} for an odd prime p > 3, is quasirecognizable by its prime graph.