The Number of Isomorphism Classes of Finite Groups with the set of Order Components of C4(q)

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 coprime 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 de...
Ausführliche Beschreibung

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 coprime 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 prove that if q=$ 2^{n} $, then the simple group C4(q) can be uniquely determined by its order components. Also if q is an odd prime power and OC(G)=OC(C4(q)), then G≅C4(q) or G≅B4(q). Ausführliche Beschreibung