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 ...
Beltran, Antonio; Felipe Román, María Josefa; Malle, Gunter; Moreto Quintana, Alexander; Navarro Ortega, Gabriel; Sanus Vitoria, Lucia; Solomon, Ronald; Tiep, Pham Huu(American Mathematical Society, 2016-04)
[EN] We give a characterization of the finite groups having nilpotent or abelian Hall pi-subgroups that can easily be verified using the character table.
Beltran, Antonio; Felipe Román, María Josefa; Melchor, Carmen(Cambridge University Press (CUP), 2016-10)
Let G be a finite group and let N be a normal subgroup of G. We determine the structure of N when the diameter of the graph associated to the G-conjugacy classes contained in N is as large as possible, that is, equal to three.
Beltran, Antonio; Felipe Román, María Josefa; Melchor, Carmen(University of Isfahan, 2020-03)
[EN] We summarize several results about non-simplicity, solvability and normal structure of finite groups related to the number of conjugacy classes appearing in the product or the power of conjugacy classes. We also collect ...