Diego García-Lucas

most citedOn group invariants determined by modular group algebras: even versus odd characteristic

1 citations · 1 across the 5 of their papers we have counts for

collaborators

5 papers

math.GR2023

On the modular isomorphism problem for groups of nilpotency class 2 with cyclic center

Diego García-Lucas, Leo Margolis

We show that the modular isomorphism problem has a positive answer for groups of nilpotency class 2 with cyclic center, i.e. that for such p-groups G and H an isomorphism between t…

math.GR2023

The Gruenberg-Kegel graph of finite solvable rational groups

Sara C. Debón, Diego García-Lucas, Ángel del Río

A finite group $G$ is said to be rational if every character of $G$ is rational-valued. The Gruenberg-Kegel graph of a finite group $G$ is the undirected graph whose vertices are t…

math.RT2023

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…

math.GR2022★ 1 cited

On group invariants determined by modular group algebras: even versus odd characteristic

Diego García-Lucas, Ángel del Río, Mima Stanojkovski

Let $p$ be a an odd prime and let $G$ be a finite $p$ -group with cyclic commutator subgroup $G^{'}$ . We prove that the exponent and the abelianization of the centralizer of $G^{'}$ in $G…

math.GR2022

The modular isomorphism problem and abelian direct factors

Diego García-Lucas

Let $p$ be a prime and let $G$ be a finite $p$ -group. We show that the isomorphism type of the maximal abelian direct factor of $G$ , as well as the isomorphism type of the group al…