On the Set of the Numbers of Conjugates of Noncyclic Proper Subgroups of Finite Groups

الملخص EN

Let G be a finite group and ??(G) the set of the numbers of conjugates of noncyclic proper subgroups of G.

We prove that (1) if |??(G)|≤2, then G is solvable, and (2) G is a nonsolvable group with |??(G)|=3 if and only if G≅PSL(2,5) or PSL(2,13) or SL(2,5) or SL(2,13).