Nilpotency of normal subgroups having two G-class sizes

Felipe Román María José, ANTONIO BELTRÁN FELIP, Alemany Martínez Elena

2011

Proceedings of the American Mathematical Society

Let G be a finite group. If N is a normal subgroup which has exactly two G-conjugacy class sizes, then N is nilpotent. In particular, we show that N is abelian or is the product of a p-group P by a central subgroup of G. Furthermore, when P is not abelian, P/(Z(G) ¿ P) has exponent p. © 2010 American Mathematical Society.