C. Melchor

collaborators

9 papers

math.GR2024

An Arad and Fisman's theorem on products of conjugacy classes revisited

Antonio BeltrÃ¡n, MarÃa JosÃ© Felipe, Carmen Melchor

A theorem of Z. Arad and E. Fisman establishes that if $A$ and $B$ are two conjugacy classes of a finite group $G$ such that either $A B = A \cup B$ or $A B = A^{- 1} \cup B$ , then $G$ can…

math.GR2024

Some problems about products of conjugacy classes in finite groups

Antonio BeltrÃ¡n, MarÃa JosÃ© Felipe, Carmen Melchor

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 powe…

math.GR2024

Landau's Theorem on conjugacy classes for normal subgroups

Antonio BeltrÃ¡n, MarÃa JosÃ© Felipe, Carmen Melchor

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 $k$ . W…

math.GR2024

Normal subgroups whose conjugacy class graph has diameter three

Antonio BeltrÃ¡n, MarÃa JosÃ© Felipe, Carmen Melchor

Let $G$ be a finite group and $N$ 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…

math.GR2024

Powers of conjugacy classes in a finite group

Many results have been established that 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 i…

math.GR2024

Multiplying a conjugacy class by its inverse in a finite group

Suppose that $G$ is a finite group and $K$ a non-trivial conjugacy class of $G$ such that $K K^{- 1} = 1 \cup D \cup D^{- 1}$ with $D$ a conjugacy class of $G$ . We prove that $G$ is not a…