Beltrán Felip, Antonio; Felipe Román, María José; Melchor, Carmen(Springer-Verlag, 2022-12)
[EN] A theorem of Z. Arad and E. Fisman establishes that if A and B are two non-trivial conjugacy classes of a finite group G such that either AB = A boolean OR B or AB = A(-1) boolean OR B, then G cannot be a non-abelian ...
Beltrán, Antonio; Felipe, María José; Melchor, Carmen(University of Isfahan, 2018)
[EN] We survey known results concerning how the conjugacy classes contained in a normal subgroup and their sizes exert an influence on the normal structure of a finite group. The approach is mainly presented in the framework ...
Beltrán, Antonio; Felipe Román, María Josefa; Melchor, Carmen(Elsevier, 2015-12-01)
Let G be a finite group and let N be a normal subgroup of G.
We attach to N two graphs ΓG(N) and Γ∗
G(N) related to the
conjugacy classes of G contained in N and to the set of primes
dividing the sizes of these classes, ...
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 ...
Beltrán, Antonio; Felipe Román, María José; Melchor, Carmen(Springer-Verlag, 2018-08)
[EN] Suppose that G is a finite group and K is a non-trivial conjugacy class of G such that KK (-1) = 1 a D a D (-1) with D a conjugacy class of G. We prove that G is not a non-abelian simple group and we give arithmetical ...
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.
Beltrán, Antonio; Camina, Rachel Deborah; Felipe Román, María Josefa; Melchor, Carmen(Springer-Verlag, 2020-04)
[EN] The aim of this paper is to show how the number of conjugacy classes appearing in the product of classes affect the structure of a finite group. The aim of this paper was to show several results about solvability ...
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 ...
Beltrán, Antonio; Felipe Román, María Josefa; Melchor, Carmen(Springer-Verlag, 2017-01)
[EN] Let G be a finite group and N a normal subgroup of G. We determine the
structure of N when the graph G(N), which is the graph associated to the conjugacy
classes of G contained in N, has no triangles and when the graph ...