Solvable Groups With 4 Conjugate Classes Of Noncyclic Subgroups

In finite groups, we study the structure and properties of group rely on the properties of subgroup is a main direction. Let G be a finite group, δ(G) denote the number of conjugate classes of the non-cyclic subgroups of G. It is quite clear that δ(G) give a lot of information of G. In this paper, we study the soluble group G with δ(G)= 4 and the nilpotent group G with δ(G)= 7.In chapter 3, we study the soluble group G with δ(G)= 4, and get the following results.Theorem 0.1 Let G be a soluble group. If G is not nilpotent and δ(G)= 4, then dl(G)≤3. Suppose that dl(G)< 3, we also have that(1) if G’ is nilpotent, then G is a non-abelian subgroup of order q3, and...