Asymptotic invariants of residually finite just infinite groups

2024/12/19 by Andrei Jaikin‐Zapirain, Jaikin-Zapirain, Andrei, Steffen Kionke +1
Mathematics · #Geometric and Algebraic Topology #Finite Group Theory Research #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2412.14765

Abstract

Recently, Eduard Schesler and the second author constructed examples of finitely generated residually finite, hereditarily just infinite groups with positive first L²-Betti number. In contrast to their result, we show that a finitely generated residually-p just infinite group has trivial first L²-Betti number. Moreover, we prove that the normal homology rank gradient of a finitely generated, residually finite, just infinite group vanishes.

Related

• Approximating the first L²-betti number of residually finite groups
• Residual Deficiency
• Hereditarily just-infinite torsion groups with positive first ℓ²-Betti number
• A note on normal generation and generation of groups
• The rank gradient from a combinatorial viewpoint