Carlo Casolo

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20112020

most citedGroups whose character degree graph has diameter three

1 citations · 1 across the 7 of their papers we have counts for

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math.GR2020

Integrals of groups II

João Araújo, Peter J. Cameron, Carlo Casolo +2

An $in t e g r a l$ of a group $G$ is a group $H$ whose commutator subgroup is isomorphic to $G$ . This paper continues the investigation on integrals of groups started in the work arXiv:…

math.GR2018

On the character degree graph of finite groups

Zeinab Akhlaghi, Carlo Casolo, Silvio Dolfi +2

Given a finite group G, let cd(G) denote the set of degrees of the irreducible complex characters of G. The character degree graph of G is defined as the simple undirected graph wh…

math.GR2018

Integrals of groups

João Araújo, Peter J. Cameron, Carlo Casolo +1

An $in t e g r a l$ of a group $G$ is a group $H$ whose derived group (commutator subgroup) is isomorphic to $G$ . This paper discusses integrals of groups, and in particular questions ab…

math.GR2017

On the character degree graph of solvable groups

Zeinab Akhlaghi, Carlo Casolo, Silvio Dolfi +2

Let $G$ be a finite solvable group, and let $Δ(G)$ denote the \emph{prime graph} built on the set of degrees of the irreducible complex characters of $G$. A fundamental resul…

math.GR2017

Groups in which each subgroup is commensurable with a normal subgroup

Carlo Casolo, Ulderico Dardano, Silvana Rinauro

A group G is a cn-group if for each subgroup H of G there exists a normal subgroup N of G such that the index of both H and N in HN is finite. The class of cn-groups contains prope…

math.GR2016★ 1 cited

Groups whose character degree graph has diameter three

Carlo Casolo, Silvio Dolfi, Emanuele Pacifici +1

Let $G$ be a finite group, and let $Δ(G)$ denote the \emph{prime graph} built on the set of degrees of the irreducible complex characters of $G$. It is well known that, whene…

math.GR2015

Variants of theorems of Baer and Hall on finite-by-hypercentral groups

Carlo Casolo, Ulderico Dardano, Silvana Rinauro

We show that if a group $G$ has a finite normal subgroup $L$ such that $G / L$ is hypercentral, then the index of the hypercenter of $G$ is bounded by a function of the order of $L$ .…

math.GR2013

On the Fitting height of soluble groups admitting a coprime factorisation

Carlo Casolo, Enrico Jabara, Pablo Spiga

In this paper we are concerned with finite soluble groups $G$ admitting a factorisation $G = A B$ , with $A$ and $B$ proper subgroups having coprime order. We are interested in boundin…

math.GR2012

Nil-automorphisms of groups with residual properties

Carlo Casolo, Orazio Puglisi

Following Plotkin we say that the automorphism $x$ of the group $G$ is a nil-automorphism if, for every $g \in G$ , there exists $n = n (g)$ such that $[g,_{n} x] = 1$ . If the integer $n$ c…

math.GR2011

Hirsch-Plotkin radical of stability groups

Carlo Casolo, Orazio Puglisi

We study the Hirsch-Plotkin radical of stability groups of (general) subspace series of infinite dimensional vector spaces. We show that in countable dimension and some other cases…