Diego García-Lucas

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

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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.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…