Groups satisfying Kaplansky's stable finiteness conjecture

2015/01/13 by Federico Berlai, Berlai, Federico
Mathematics · #Algebraic structures and combinatorial models #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR)

paper · pdf · doi:10.48550/arxiv.1501.02893

openalex publication_date 2015/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that every finitely generated residually finite-by-sofic group satisfies Kaplansky's direct and stable finiteness conjectures with respect to all noetherian rings. We use this result to provide countably many new examples of finitely presented non-LEA groups, for which soficity is still undecided, satisfying these two conjectures. Deligne's famous example of a non residually finite group is among our examples, along with the families of amalgamated free products SL_n(Z[1/p])*_FrSL_n(Z[1/p]) and HNN extensions SL_n(Z[1/p])*_Fr, where p>2 is a prime, n>2 and F_r is a free group of rank r, for all r>1.

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