6 papers
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…
On the abscissae of Weil representation zeta functions for procyclic groups
Steffen Kionke
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…
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…
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…