5 citations · 49 across the 28 of their papers we have counts for
22 papers · 1 filter
Infinite groups from the profinite point of view
Holger Kammeyer, Steffen Kionke
We survey recent work ranging around the question in how far a group, or a property of a group, is determined by the set of finite quotient groups. Our focus lies on -arithmetic…
Asymptotic invariants of residually finite just infinite groups
Andrei Jaikin-Zapirain, Steffen Kionke
Recently, Eduard Schesler and the second author constructed examples of finitely generated residually finite, hereditarily just infinite groups with positive first -Betti numb…
Profiniteness of higher rank volume
Holger Kammeyer, Steffen Kionke, Ralf Köhl
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 r…
Hereditarily just-infinite torsion groups with positive first -Betti number
Steffen Kionke, Eduard Schesler
We present a new method to construct finitely generated, residually finite, infinite torsion groups. In contrast to known constructions, a profinite perspective enables us to contr…
Gassmann triples with special cycle types and applications
Holger Kammeyer, Steffen Kionke
We show that if one of various cycle types occurs in the permutation action of a finite group on the cosets of a given subgroup, then every almost conjugate subgroup is conjugate.…
From telescopes to frames and simple groups
Steffen Kionke, Eduard Schesler
We introduce the notion of a telescope of groups. Very roughly a telescope is a directed system of groups that contains various commuting images of some fixed group . Telescopes…
On representations of direct products and the bounded generation property of branch groups
Steffen Kionke, Eduard Schesler
We prove that the minimal representation dimension of a direct product of non-abelian groups is bounded below by and thereby answer a question of Abért.…
Realizing residually finite groups as subgroups of branch groups
Steffen Kionke, Eduard Schesler
We prove that every finitely generated, residually finite group embeds into a finitely generated perfect branch group such that many properties of are preserved under t…
Weil zeta functions of group representations over finite fields
Ged Corob Cook, Steffen Kionke, Matteo Vannacci
In this article we define and study a zeta function - similar to the Hasse-Weil zeta function - which enumerates absolutely irreducible representations over finite fields of…
On absolutely profinitely solitary lattices in higher rank Lie groups
Holger Kammeyer
We establish conditions under which lattices in certain simple Lie groups are profinitely solitary in the absolute sense, so that the commensurability class of the profinite comple…
On upper bounds for the first -Betti number
Carsten Feldkamp, Steffen Kionke
This article presents a method for proving upper bounds for the first -Betti number of groups using only the geometry of the Cayley graph. As an application we prove that B…
Counting irreducible modules for profinite groups
Ged Corob Cook, Steffen Kionke, Matteo Vannacci
This article is concerned with the representation growth of profinite groups over finite fields. We investigate the structure of groups with uniformly bounded exponential represent…
Amenability and profinite completions of finitely generated groups
Steffen Kionke, Eduard Schesler
This article explores the interplay between the finite quotients of finitely generated residually finite groups and the concept of amenability. We construct a finitely generated, r…
Adelic superrigidity and profinitely solitary lattices
Holger Kammeyer, Steffen Kionke
By arithmeticity and superrigidity, a commensurability class of lattices in a higher rank Lie group is defined by a unique algebraic group over a unique number subfield of $\mathbb…
On the profinite rigidity of lattices in higher rank Lie groups
Holger Kammeyer, Steffen Kionke
We investigate which higher rank simple Lie groups admit profinitely but not abstractly commensurable lattices. We show that no such examples exist for the complex forms of type $E…
Profinite invariants of arithmetic groups
Holger Kammeyer, Steffen Kionke, Jean Raimbault +1
We prove that the sign of the Euler characteristic of arithmetic groups with CSP is determined by the profinite completion. In contrast, we construct examples showing that this is…
Groups acting on rooted trees and their representations on the boundary
Steffen Kionke
We consider groups that act on spherically symmetric rooted trees and study the associated representation of the group on the space of locally constant functions on the boundary of…
Zeta functions associated to admissible representations of compact p-adic Lie groups
Steffen Kionke, Benjamin Klopsch
Let be a profinite group. A strongly admissible smooth representation of over decomposes as a direct sum $ρ\cong \bigoplus_{π\in \mathrm{Irr}(G)} m_π(ρ) \,…
Characters, -Betti numbers and an equivariant approximation theorem
Steffen Kionke
Let be a group with a finite subgroup . We define the -multiplicity of an irreducible representation of in the -homology of a proper -CW-complex. These inva…
Positively finitely related profinite groups
Steffen Kionke, Matteo Vannacci
We define and study the class of positively finitely related (PFR) profinite groups. Positive finite relatedness is a probabilistic property of profinite groups which provides a fi…
On geometric aspects of diffuse groups
Steffen Kionke, Jean Raimbault, Nathan Dunfield
Bowditch introduced the notion of diffuse groups as a geometric variation of the unique product property. We elaborate on various examples and non-examples, keeping the geometric p…
On lower bounds for cohomology growth in p-adic analytic towers
Steffen Kionke
Let p and l be two distinct prime numbers and let G be a group. We study the asymptotic behaviour of the mod-l Betti numbers in p-adic analytic towers of finite index subgroups. If…