6 papers
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…
Integrals of groups
João Araújo, Peter J. Cameron, Carlo Casolo +1
An of a group is a group whose derived group (commutator subgroup) is isomorphic to . This paper discusses integrals of groups, and in particular questions ab…
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…
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…
Variants of theorems of Baer and Hall on finite-by-hypercentral groups
Carlo Casolo, Ulderico Dardano, Silvana Rinauro
We show that if a group has a finite normal subgroup such that is hypercentral, then the index of the hypercenter of is bounded by a function of the order of .…
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…