Asymptotic invariants of residually finite just infinite groups
Group Theory
2024-12-20 v1
Abstract
Recently, Eduard Schesler and the second author constructed examples of finitely generated residually finite, hereditarily just infinite groups with positive first -Betti number. In contrast to their result, we show that a finitely generated residually- just infinite group has trivial first -Betti number. Moreover, we prove that the normal homology rank gradient of a finitely generated, residually finite, just infinite group vanishes.
Cite
@article{arxiv.2412.14765,
title = {Asymptotic invariants of residually finite just infinite groups},
author = {Andrei Jaikin-Zapirain and Steffen Kionke},
journal= {arXiv preprint arXiv:2412.14765},
year = {2024}
}
Comments
to appear in a special issue of the European Journal of Mathematics dedicated to Nikolay Vavilov