R. Camina

collaborators

5 papers

math.GR2025

Groups with conjugacy classes of coprime sizes

Rachel D. Camina, Attila MarÃ³ti, Emanuele Pacifici +6

Suppose that $x$ , $y$ are elements of a finite group $G$ lying in conjugacy classes of coprime sizes. We prove that $⟨ x^{G} ⟩ \cap ⟨ y^{G} ⟩$ is an abelian nor…

math.GR2025

Group cosets with all elements of equal order

Alan R. Camina, Rachel D. Camina, Mark L. Lewis +3

Let $G$ be a finite group and $N$ a proper, nontrivial, normal subgroup of $G$ . If, for every element $x$ of $G$ not lying in $N$ , the elements in the coset $x N$ all have the same…

math.GR2025

On groups that can be covered by conjugates of finitely many cyclic or procyclic subgroups

Yiftach Barnea, Rachel Camina, Mikhail Ershov +1

Given a discrete (resp. profinite) group $G$ , we define $N C C (G)$ to be the smallest number of cyclic (resp. procyclic) subgroups of $G$ whose conjugates cover $G$ . In this paper we…

math.GR2025

Semi-extraspecial $p$ -groups with automorphisms of large order

Sofia Brenner, Rachel D. Camina, Mark L. Lewis

In this paper, we consider semi-extraspecial $p$ -groups $G$ that have an automorphism of order $∣ G : G^{'} ∣ - 1$ . We prove that these groups are isomorphic to Sylow $p$ -subgroups of ${\…

math.GR2024

On non self-normalizing subgroups

Mariagrazia Bianchi, Rachel D. Camina, Mark L. Lewis +2

Let $n$ be a non negative integer, and define $D_{n}$ to be the family of all finite groups having precisely $n$ conjugacy classes of nontrivial subgroups that are not self-normalizi…

Groups with conjugacy classes of coprime sizes

Group cosets with all elements of equal order

On groups that can be covered by conjugates of finitely many cyclic or procyclic subgroups

Semi-extraspecial p-groups with automorphisms of large order

On non self-normalizing subgroups

Semi-extraspecial $p$ -groups with automorphisms of large order