R. Camina

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20172022

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math.GR2022

Conjugacy classes of maximal cyclic subgroups and nilpotence class of $p$ -groups

M. Bianchi, R. D. Camina, Mark L. Lewis

In this paper, we set $η (G)$ to be the number of conjugacy classes of maximal cyclic subgroups of $G$ . We prove that if $G$ is a $p$ -group of order $p^{n}$ and nilpotence class $l$ ,…

math.GR2022

Conjugacy classes of maximal cyclic subgroups

M. Bianchi, R. D. Camina, Mark L. Lewis +1

In this paper, we set $η (G)$ to be the number of conjugacy classes of maximal cyclic subgroups of $G$ . We consider $η$ and direct and semi-direct products. We characterize the norm…

math.GR2020

Restrictions on sets of conjugacy class sizes in arithmetic progressions

Alan R. Camina, Rachel D. Camina

We continue the investigation, that began in [3] and [4], into finite groups whose set of nontrivial conjugacy class sizes form an arithmetic progression. Let $G$ be a finite group…

math.GR2020

Word problems for finite nilpotent groups

Rachel D. Camina, Ainhoa Iniguez, Anitha Thillaisundaram

Let $w$ be a word in $k$ variables. For a finite nilpotent group $G$ , a conjecture of Amit states that $N_{w} (1) \geq ∣ G ∣^{k - 1}$ , where $N_{w} (1)$ is the number of $k$ -tuples $(g_1,...,…

math.GR2020

On solvable groups with one vanishing class size

Mariagrazia Bianchi, Rachel D. Camina, Mark L. Lewis +1

Let $G$ be a finite group, and let cs $(G)$ be the set of conjugacy class sizes of $G$ . Recalling that an element $g$ of $G$ is called a \emph{vanishing element} if there exists an…

math.GR2017

On vanishing class sizes in finite groups

Mariagrazia Bianchi, Julian M. A. Brough, Rachel D. Camina +1

Let $G$ be a finite group. An element $g$ of $G$ is called a vanishing element if there exists an irreducible character $χ$ of $G$ such that $χ (g) = 0$ ; in this case, we say that t…

Conjugacy classes of maximal cyclic subgroups and nilpotence class of p-groups

Conjugacy classes of maximal cyclic subgroups

Restrictions on sets of conjugacy class sizes in arithmetic progressions

Word problems for finite nilpotent groups

On solvable groups with one vanishing class size

On vanishing class sizes in finite groups

Conjugacy classes of maximal cyclic subgroups and nilpotence class of $p$ -groups