Beltran, Antonio; Felipe Román, María José; Melchor, Carmen(World Scientific Publishing, 2016-11)
Landau's theorem on conjugacy classes asserts that there are only finitely many finite groups, up to isomorphism, with exactly k conjugacy classes for any positive integer k. We show that, for any positive integers n and ...
Alemany Martínez, Elena; Beltran, Antonio; Felipe Román, María José(American Mathematical Society, 2011)
[EN] 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 ...
Beltrán, Antonio; Felipe Román, María José(American Mathematical Society, 2012)
[EN] If G is a finite group and N is a normal subgroup of G with two C-conjugacy class sizes of elements of prime power order, then we show that N is nilpotent.