title: On the set of the numbers of conjugates of noncyclic proper subgroups of finite groups.
abstract: Let G be a finite group and N C (G) the set of the numbers of conjugates of noncyclic proper subgroups of G. We prove that (1) if |N C G)| ≤ 2, then G is solvable, and (2) G is a nonsolvable group with |N C (G)| = 3 if and only if G≅PSL(2,5) or PSL(2,13) or SL(2,5) or SL(2,13).
authors.affiliation: School of Mathematics and Information Science, Yantai University, Yantai 264005, China.
authors.forename: Jiangtao
authors.initials: J
authors.lastname: Shi
authors.forename: Cui
authors.initials: C
authors.lastname: Zhang
mesh_terms: D055641:Mathematical Concepts; D008433:Mathematics / Q000379:methods*; D008962:Models, Theoretical