Zobrazeno 1 - 10
of 839
pro vyhledávání: '"20E18"'
We show that the covolume of an irreducible lattice in a higher rank semisimple Lie group with the congruence subgroup property is determined by the profinite completion. Without relying on CSP, we additionally show that volume is a profinite invaria
Externí odkaz:
http://arxiv.org/abs/2412.13056
Autor:
Xu, Xiaoyu
Any profinite isomorphism between two cusped finite-volume hyperbolic 3-manifolds carries profinite isomorphisms between their Dehn fillings. With this observation, we prove that some cusped finite-volume hyperbolic 3-manifolds are profinitely rigid
Externí odkaz:
http://arxiv.org/abs/2412.05229
Autor:
Kionke, Steffen
A famous conjecture of Chowla on the least primes in arithmetic progressions implies that the abscissa of convergence of the Weil representation zeta function for a procyclic group $G$ only depends on the set $S$ of primes dividing the order of $G$ a
Externí odkaz:
http://arxiv.org/abs/2411.12848
Using methods of associative algebras, Lie theory, group cohomology, and modular representation theory, we construct profinite $p$-adic analytic groups such that the centralizer of each of their non-trivial elements is abelian. The paper answers ques
Externí odkaz:
http://arxiv.org/abs/2411.03880
Autor:
Livramento, Karina, Noseda, Francesco
We exhibit infinite lists of ramification indices $\delta$ for which the classical Lie groups over the ring of integers of $p$-adic fields admit a faithful self-similar action on a regular rooted $\delta$-ary tree in such a way that the action is tra
Externí odkaz:
http://arxiv.org/abs/2410.22639
Autor:
Xu, Xiaoyu
We prove that any compact, orientable 3-manifold with empty or toral boundary is profinitely almost rigid among all compact, orientable 3-manifolds, i.e. the profinite completion of its fundamental group determines its homeomorphism type to finitely
Externí odkaz:
http://arxiv.org/abs/2410.16002
Autor:
Blachar, Guy
We show that the lamplighter groups $(\mathbb{Z}/p\mathbb{Z})^n\wr\mathbb{Z}$, where $p$ is prime and $n\ge 1$ is a positive integer, are profinitely rigid.
Comment: 6 pages. Comments are welcome!
Comment: 6 pages. Comments are welcome!
Externí odkaz:
http://arxiv.org/abs/2410.15945
Autor:
Khukhro, Evgeny, Shumyatsky, Pavel
A right Engel sink of an element $g$ of a group $G$ is a subset containing all sufficiently long commutators $[...[[g,x],x],\dots ,x]$. We prove that if $G$ is a compact group in which, for some $k$, every commutator $[...[g_1,g_2],\dots ,g_k]$ has a
Externí odkaz:
http://arxiv.org/abs/2410.05840
Autor:
Bridson, Martin R., Piwek, Paweł
A free-by-cyclic group $F_N\rtimes_\phi\mathbb{Z}$ has non-trivial centre if and only if $[\phi]$ has finite order in ${\rm{Out}}(F_N)$. We establish a profinite ridigity result for such groups: if $\Gamma_1$ is a free-by-cyclic group with non-trivia
Externí odkaz:
http://arxiv.org/abs/2409.20513
Autor:
Wilkes, Gareth
The well-known theory of Pontryagin duality provides a strong connection between the homology and cohomology theories of a profinite group in appropriate categories. A construction for taking the `profinite direct sum' of an infinite family of profin
Externí odkaz:
http://arxiv.org/abs/2408.13059