Recognizability of the Simple $K_n$-Groups ($n=3, 4$)

Abstract

Let $G$ be a finite group. Based on the prime graph of $G$, the order of $G$ can be divided into a product of co-prime positive integers. These integers are called order components of $G$ and the set of order components is denoted by $OC(G)$. Some non-abelian simple groups are known to be uniquely determined by their order components. In this paper we discuss the recognizability of simple $K_n$-groups ($n=3, 4$) by their order components.