Zobrazeno 1 - 10
of 309
pro vyhledávání: '"A, Jaikin"'
Autor:
Jaikin-Zapirain, Andrei
In this paper, we introduce the notion of $L^2$-subgroup rigid groups and demonstrate that free groups are $L^2$-subgroup rigid. As a consequence, we establish the equivalence between compressibility, inertness, strong inertness, and $L^2$-independen
Externí odkaz:
http://arxiv.org/abs/2403.09515
Let $G$ be a finitely generated torsion-free pro-$p$ group containing an open free-by-$\mathbb{Z}_p$ pro-$p$ subgroup. We show that the completed group algebra of $G$ over $\mathbb{F}_p$ is a Sylvester domain. Moreover the inner rank of a matrix $A$
Externí odkaz:
http://arxiv.org/abs/2402.14130
We revisit the paper of Alexander Grothendiek where he introduced Grothendieck pairs and discuss the relation between profinite rigidity and left/right Grothendieck rigidity. We also show that various groups are left and/or right Grothendieck rigid a
Externí odkaz:
http://arxiv.org/abs/2401.02229
Surface groups are known to be the Poincar\'e Duality groups of dimension two since the work of Eckmann, Linnell and M\"uller. We prove a prosolvable analogue of this result that allows us to show that surface groups are profinitely (and prosolvably)
Externí odkaz:
http://arxiv.org/abs/2312.12293
Autor:
Jaikin-Zapirain, Andrei, Linton, Marco
We prove that one-relator groups are coherent, solving a well-known problem of Gilbert Baumslag. Our proof strategy is readily applicable to many classes of groups of cohomological dimension two. We show that fundamental groups of two-complexes with
Externí odkaz:
http://arxiv.org/abs/2303.05976
Autor:
Jaikin-Zapirain, Andrei
We develop a method to show that some (abstract) groups can be embedded into a free pro-$p$ group. In particular, we show that a finitely generated subgroup of a free $\mathbb Q$-group can be embedded into a free pro-$p$ group for almost all primes $
Externí odkaz:
http://arxiv.org/abs/2212.00402
Publikováno v:
International Mathematics Research Notices, Volume 2023, Issue 24, December 2023, Pages 21320--21345
Can one detect free products of groups via their profinite completions? We answer positively among virtually free groups. More precisely, we prove that a subgroup of a finitely generated virtually free group $G$ is a free factor if and only if its cl
Externí odkaz:
http://arxiv.org/abs/2207.00912
Wolfang L\"uck asked if twisted $L^2$-Betti numbers of a group are equal to the usual $L^2$-Betti numbers rescaled by the dimension of the twisting representation. We confirm this for sofic groups.
Comment: 8 Pages, accepted for publication in t
Comment: 8 Pages, accepted for publication in t
Externí odkaz:
http://arxiv.org/abs/2201.03268
We establish a combination theorem for parafree groups. These groups were introduced by Baumslag in the sixties. One of the current motivations for a better understanding of their structure is that they show up naturally in connection with Remeslenni
Externí odkaz:
http://arxiv.org/abs/2110.11655
Given a ring $R$, the notion of Sylvester rank function was conceived within the context of Cohn's classification theory of epic division $R$-rings. In this paper we study and describe the space of Sylvester rank functions on certain families of ring
Externí odkaz:
http://arxiv.org/abs/2012.15844