2 citations · 2 across the 11 of their papers we have counts for
12 papers
The Gruenberg-Kegel graph of finite solvable groups that are character-quadratic or semi-rational
Irene Crispi, Sara C. Debón, Emanuele Pacifici +2
A finite group is said to be semi-rational if the set of generators of each cyclic subgroup of is contained in at most two -conjugacy classes. This is equivalent to the…
Gruenberg-Kegel graphs with four edges of finite solvable cut groups
Sara C. Debón, Diego García-Lucas, Ángel del Río
We prove that there is a unique graph with four edges which is the Gruenberg-Kegel graph of a solvable cut group. This contributes to the classification of the Gruenberg-Kegel grap…
Groupoid graded rings and their categories of graded modules
Caio Antony, Ángel del Río
Let be a groupoid acting on a set and let be a -graded ring with graded local units. We study the main properties of the category of -graded -modu…
Uniformly semi-rational groups
Ángel del Río, Marco Vergani
We introduce and study some families of groups whose irreducible characters take values on quadratic extensions of the rationals. We focus mostly on a generalization of inverse sem…
The Gruenberg-Kegel graph of finite solvable rational groups
Sara C. Debón, Diego García-Lucas, Ángel del Río
A finite group is said to be rational if every character of is rational-valued. The Gruenberg-Kegel graph of a finite group is the undirected graph whose vertices are t…
A classification of metacyclic groups by group invariants
Àngel García-Blázquez, Ángel del Río
We obtain a new classification of the finite metacyclic group in terms of group invariants. We present an algorithm to compute these invariants, and hence to decide if two given fi…
The isomorphism problem for rational group algebras of finite metacyclic nilpotent groups
Àngel García-Blázquez, Ángel del Río
We prove that if and are finite metacyclic groups with isomorphic rational group algebras and one of them is nilpotent then and are isomorphic.
Finite Subgroups of Group Rings: A survey
Leo Margolis, Ángel del Río
In the 1940's Graham Higman initiated the study of finite subgroups of the unit group of an integral group ring. Since then many fascinating aspects of this structure have been dis…
Zassenhaus Conjecture on torsion units holds for and
Ángel del Río, Mariano Serrano
H.J. Zassenhaus conjectured that any unit of finite order and augmentation in the integral group ring of a finite group is conjugate in the rational group alg…
Revisiting Poincaré's Theorem on presentations of discontinuous groups via fundamental polyhedra
Eric Jespers, Ann Kiefer, Ángel del Río
We give a new self-contained proof of Poincaré's Polyhedron Theorem on presentations of discontinuous groups of isometries of a Riemann manifold of constant curvature. The proof is…
Bass units as free factors in integral group rings of simple groups
Jairo Z. Gonçalves, Robert M. Guralnick, Ángel del Río
Let be a finite group, a Bass unit based on an element of of prime order, and assume that has infinite order modulo the center of the units of the integral grou…
Group rings of finite strongly monomial groups: central units and primitive idempotents
Eric Jespers, Gabriela Olteanu, Ángel del Río +1
We compute the rank of the group of central units in the integral group ring of a finite strongly monomial group . The formula obtained is in terms of the strong Shoda pa…