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

Abstract

Let G be a finite group and let Γ(G) be the prime graph of G. We assume that n ≥ 17 is an odd number. In this paper, we show that if Γ(G) = Γ(Cn(4)), then G has a unique non-abelian composition factor isomorphic to Cn(4). As consequences of our result, Cn(4) is quasirecognizable by its spectrum.