9 citations · 19 across the 15 of their papers we have counts for
18 papers
An intrinsical description of group codes
José Joaquín Bernal, Ángel del Río, Juan Jacobo Simón
A (left) group code of length n is a linear code which is the image of a (left) ideal of a group algebra via an isomorphism from FG to Fn which maps G to the standard basis of Fn.…
On the Modular Isomorphism Problem for 2-generated groups with cyclic derived subgroup
Diego García-Lucas, Ángel del Río
We continue the analysis of the Modular Isomorphism Problem for -generated -groups with cyclic derived subgroup, , started in [D. García-Lucas, Á. del Río, and M. Stanoj…
The isomorphism problem for rational group algebras of finite metacyclic groups
Ángel del Río, Àngel García-Blázquez
We prove that if two finite metacyclic groups have isomorphic rational group algebras, then they are isomorphic. This contributes to understand where is the line separating positiv…
A reduction theorem for the isomorphism problem of group algebras over fields
Diego García-Lucas, Ángel del Río
We prove that the isomorphism problem for group algebras reduces to group algebras over finite extensions of the prime field. In particular, the modular isomorphism problem reduces…
Gruenberg-Kegel graphs: cut groups, rational groups and the Prime Graph Question
Andreas Bächle, Ann Kiefer, Sugandha Maheshwary +1
The Gruenberg-Kegel graph of a group is the undirected graph whose vertices are those primes which occur as the order of an element of the group, and distinct vertices , are…
Non-isomorphic 2-groups with isomorphic modular group algebras
Diego García, Leo Margolis, Ángel del Río
We provide non-isomorphic finite 2-groups which have isomorphic group algebras over any field of characteristic 2, thus settling the Modular Isomorphism Problem.
Finite groups in integral group rings
Ángel del Río
Notes used for a course held in 2016 in the School of Advances in Group Theory and Applications, for some lectures given in 2018 for the students of the Master in Mathematics of th…
Partial Augmentations Power property: A Zassenhaus Conjecture related problem
Leo Margolis, Ángel del Río
Zassenhaus conjectured that any unit of finite order in the integral group ring of a finite group is conjugate in the rational group algebra of to an element…
Zassenhaus Conjecture on torsion units holds for with a Fermat or Mersenne prime
Leo Margolis, Ángel del Río, Mariano Serrano
H.J. Zassenhaus conjectured that any unit of finite order in the integral group ring of a finite group is conjugate in the rational group algebra to…
On the torsion units of the integral group ring of finite projective special linear groups
Ángel del Río, Mariano Serrano
H. J. Zassenhaus conjectured that any unit of finite order and augmentation one in the integral group ring of a finite group is conjugate in the rational group algebra to an el…
Polynomials defining many units
Osnel Broche, Ángel del Río
We classify the polynomials with integral coefficients that, when evaluated on a group element of finite order , define a unit in the integral group ring for infinitely many pos…
Group rings with Lie metabelian set of symmetric elements
Osnel Broche, Ángel del Río, Manuel Ruiz
Let be a commutative ring of characteristic zero and an arbitrary group. In the present paper we classify the groups for which the set of symmetric elements with respec…
On the Congruence Subgroup Problem for integral group rings
Mauricio Caicedo, Ángel del Río
Let be a finite group, the integral group ring of and $\U(\Z G)$ the group of units of . The Congruence Subgroup Problem for $\U(\Z G)$ is the problem of decid…
Central units of integral group rings
Eric Jespers, Gabriela Olteanu, Ángel del Río +1
We give an explicit description for a basis of a subgroup of finite index in the group of central units of the integral group ring of a finite abelian-by-supersolvable group…
Zassenhaus conjecture for cyclic-by-abelian groups
Mauricio Caicedo, Leo Margolis, Ángel del Río
Zassenhaus Conjecture for torsion units states that every augmentation one torsion unit of the integral group ring of a finite group G is conjugate to an element of G in the units…
Writing units of integral group rings of finite abelian groups as a product of Bass units
Eric Jespers, Ángel del Río, Inneke Van Gelder
We give a constructive proof of the theorem of Bass and Milnor saying that if is a finite abelian group then the Bass units of the integral group ring generate a subgrou…
Rational group algebras of finite groups: from idempotents to units of integral group rings
E. Jespers, G. Olteanu, A. del Rio
We give an explicit and character-free construction of a complete set of orthogonal primitive idempotents of a rational group algebra of a finite nilpotent group and a full descrip…
Every projective Schur algebra is Brauer equivalent to a radical abelian algebra
Eli Aljadeff, Ángel del Río
We prove that any projective Schur algebra over a field is equivalent in to a radical abelian algebra. This was conjectured in 1995 by Sonn and the first author of this…