Zobrazeno 1 - 10
of 271
pro vyhledávání: '"del Río, Ángel"'
We prove that any tensor product factorization with a commutative factor of a modular group algebra over a prime field comes from a direct product decomposition of the group basis. This extends previous work by Carlson and Kov\'acs for the commutativ
Externí odkaz:
http://arxiv.org/abs/2408.09036
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. Many classical linear codes have been shown to be group codes. In this
Externí odkaz:
http://arxiv.org/abs/2402.02983
Autor:
García-Lucas, Diego, del Río, Ángel
We continue the analysis of the Modular Isomorphism Problem for $2$-generated $p$-groups with cyclic derived subgroup, $p>2$, started in [D. Garc\'ia-Lucas, \'A. del R\'io, and M. Stanojkovski. On group invariants determined by modular group algebras
Externí odkaz:
http://arxiv.org/abs/2310.02627
Autor:
del Río, Ángel, García-Blázquez, Àngel
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 positive and negative solutions to the Isomorphism Problem for group algebras
Externí odkaz:
http://arxiv.org/abs/2308.00432
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 the primes dividing the order of $G$ and the edges join different prime
Externí odkaz:
http://arxiv.org/abs/2306.12883
Autor:
García-Lucas, Diego, del Río, Ángel
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 to finite modular group algebras.
Comment: 5 pages, minor revisi
Comment: 5 pages, minor revisi
Externí odkaz:
http://arxiv.org/abs/2305.09355
We establish that standard arithmetic subgroups of a special orthogonal group ${\rm SO}(1,n)$ are conjugacy separable. As an application we deduce this property for unit groups of certain integer group rings. We also prove that finite quotients of gr
Externí odkaz:
http://arxiv.org/abs/2302.09375
Autor:
García-Blázquez, Àngel, del Río, Ángel
We prove that if $G$ and $H$ are finite metacyclic groups with isomorphic rational group algebras and one of them is nilpotent then $G$ and $H$ are isomorphic.
Comment: 16 pages. Some typos fixed
Comment: 16 pages. Some typos fixed
Externí odkaz:
http://arxiv.org/abs/2301.09463
Autor:
García-Blázquez, Àngel, del Río, Ángel
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 finite metacyclic groups are isomorphic, and another algorithm which com
Externí odkaz:
http://arxiv.org/abs/2301.08683
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 $G$ are determined by the group algebra of $G$ over any field of charact
Externí odkaz:
http://arxiv.org/abs/2209.06143