Volume 34 • Number 3 • 2011
 • Quasirecognition by the Prime Graph of the Group $C_n(2)$, Where $n\neq 3$ is Odd Mahnaz Foroudi Ghasemabadi and Ali Iranmanesh Abstract. Let $G$ be a finite group and let $\Gamma(G)$ be the prime graph of $G$. We assume that $n$ is an odd number. In this paper, we show that if $\Gamma(G)=\Gamma(C_n(2))$, where $n\neq 3$, then $G$ has a unique nonabelian composition factor isomorphic to $C_n(2)$. As consequences of our result, $C_n(2)$ is quasirecognizable by its spectrum and by a new proof the validity of a conjecture of W. J. Shi for $C_n(2)$ is obtained. 2010 Mathematics Subject Classification: 20D05, 20D06, 20D60. Full text: PDF