Solvability of normal subgroups and $G$-class sizes

Abstract

Debreceni egyetem matematika intézet Beltrán, A.; Felipe Román, MJ. (2013) Abstract. We study the solvability of a normal subgroup N of a finite group G having exactly three G-conjugacy class sizes. We show that if the set of G-class sizes of N is {1, m, mp a }, with p a prime not dividing m, then N is solvable. Thus, we get a partial extension for normal subgroups on N. Itô's theorem on the solvability of groups having exactly three class sizes.