Valentina Grazian

activity

20172026

most citedA conjecture related to the nilpotency of groups with isomorphic non-commuting graphs

4 citations · 19 across the 13 of their papers we have counts for

collaborators

16 papers

math.GR2026

Modules with few Jordan blocks for rank $1$ groups of Lie type and related groups

Valentina Grazian, Justin Lynd, Chris Parker +2

Suppose that $p$ is a prime and $X$ is a finite group with a strongly $p$ -embedded subgroup, for example a rank $1$ group of Lie type in characteristic $p$ . Let $m$ denote the $p$ -…

math.GR2025

On finite groups with soluble centralisers

Valentina Grazian, Carmine Monetta, Gareth Tracey

We classify finite groups in which the centralisers of certain non-central elements are soluble. This includes a full structural description of groups whose non-central element cen…

math.GR2025

Fusion systems related to polynomial representations of $SL_{2} (q)$

Valentina Grazian, Chris Parker, Jason Semeraro +1

Let $q$ be a power of a fixed prime $p$ . We classify up to isomorphism all simple saturated fusion systems on a certain class of $p$ -groups constructed from the polynomial represen…

math.GR2023★ 3 cited

Group nilpotency from a graph point of view

Valentina Grazian, Andrea Lucchini, Carmine Monetta

Let $Γ_{G}$ denote a graph associated with a group $G$ . A compelling question about finite groups asks whether or not a finite group $H$ must be nilpotent provided $Γ_{H}$ is isomorphi…

math.GR2023★ 4 cited

A conjecture related to the nilpotency of groups with isomorphic non-commuting graphs

Valentina Grazian, Carmine Monetta

In this work we discuss whether the non-commuting graph of a finite group can determine its nilpotency. More precisely, Abdollahi, Akbari and Maimani conjectured that if $G$ and $H…

math.CO2023★ 1 cited

On the order of semiregular automorphisms of cubic vertex-transitive graphs

Marco Barbieri, Valentina Grazian, Pablo Spiga

We prove that, if $Γ$ is a finite connected cubic vertex-transitive graph, then either there exists a semiregular automorphism of $Γ$ of order at least $6$ , or the number of vertic…

math.GR2022

On the structure of finite groups determined by the arithmetic and geometric means of element orders

Valentina Grazian, Carmine Monetta, Marialaura Noce

In this paper we consider two functions related to the arithmetic and geometric means of element orders of a finite group, showing that certain lower bounds on such functions stron…

math.GR2022

Sharpness of saturated fusion systems on a Sylow $p$ -subgroup of $G_{2} (p)$

Valentina Grazian, Ettore Marmo

We prove that the Díaz-Park's sharpness conjecture holds for saturated fusion systems defined on a Sylow $p$ -subgroup of the group $G_{2} (p)$ , for $p \geq 5$ .

math.CO2022★ 3 cited

On the number of fixed edges of automorphisms of vertex-transitive graphs of small valency

Marco Barbieri, Valentina Grazian, Pablo Spiga

We prove that, if $Γ$ is a finite connected $3$ -valent vertex-transitive, or $4$ -valent vertex- and edge-transitive graph, then either $Γ$ is part of a well-understood family of gr…

math.CO2022★ 2 cited

On the Cayleyness of Praeger-Xu graphs

Marco Barbieri, Valentina Grazian, Pablo Spiga

We give a sufficient and necessary condition for a Praeger-Xu graph to be a Cayley graph.

math.GR2021

Kernels of Localities

Valentina Grazian, Ellen Henke

We state a sufficient condition for a fusion system to be saturated. This is then used to investigate localities with kernels, i.e. localities which are (in a particular way) exten…

math.GR2021★ 3 cited

$p$ -nilpotency criteria for some verbal subgroups

Yerko Contreras Rojas, Valentina Grazian, Carmine Monetta

Let $G$ be a finite group, let $p$ be a prime and let $w$ be a group-word. We say that $G$ satisfies $P (w, p)$ if the prime $p$ divides the order of $x y$ for every $w$ -value $x$ in…

math.GR2020★ 3 cited

Saturated fusion systems on $p$ -groups of maximal class

Valentina Grazian, Christopher Parker

For a prime number $p$ , a finite $p$ -group of order $p^{n}$ has maximal class if it has nilpotency class $n - 1$ . Here we examine saturated fusion systems on maximal class $p$ -groups a…

math.GR2019

Semidirect Products and Wreath Products of Localities

Valentina Grazian, Ellen Henke

We develop a theory of semidirect products of partial groups and localities. Our concepts generalize the notions of direct products of partial groups and localities, and of semidir…

math.GR2018

Fusion systems on p-groups of sectional rank 3

Valentina Grazian

We study saturated fusion systems on $p$ -groups having sectional rank $3$ for all odd primes $p$ . For $p \geq 5$ , we obtain a complete classification of the ones that do not have an…

math.GR2017

Fusion systems containing pearls

Valentina Grazian

An $F$ -essential subgroup is called a pearl if it is either elementary abelian of order $p^{2}$ or non-abelian of order $p^{3}$ . In this paper we start the investigation of f…

Modules with few Jordan blocks for rank 1 groups of Lie type and related groups

On finite groups with soluble centralisers

Fusion systems related to polynomial representations of SL2​(q)

Group nilpotency from a graph point of view

A conjecture related to the nilpotency of groups with isomorphic non-commuting graphs

On the order of semiregular automorphisms of cubic vertex-transitive graphs

On the structure of finite groups determined by the arithmetic and geometric means of element orders

Sharpness of saturated fusion systems on a Sylow p-subgroup of G2​(p)

On the number of fixed edges of automorphisms of vertex-transitive graphs of small valency

On the Cayleyness of Praeger-Xu graphs

Kernels of Localities

p-nilpotency criteria for some verbal subgroups

Saturated fusion systems on p-groups of maximal class

Semidirect Products and Wreath Products of Localities

Fusion systems on p-groups of sectional rank 3

Fusion systems containing pearls

Modules with few Jordan blocks for rank $1$ groups of Lie type and related groups

Fusion systems related to polynomial representations of $SL_{2} (q)$

Sharpness of saturated fusion systems on a Sylow $p$ -subgroup of $G_{2} (p)$

$p$ -nilpotency criteria for some verbal subgroups

Saturated fusion systems on $p$ -groups of maximal class