Groups satisfying Kaplansky's stable finiteness conjecture
Group Theory
2015-01-14 v1
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])*_{F_r}SL_n(Z[1/p]) and HNN extensions SL_n(Z[1/p])*_{F_r}, where p>2 is a prime, n>2 and F_r is a free group of rank r, for all r>1.
Keywords
Cite
@article{arxiv.1501.02893,
title = {Groups satisfying Kaplansky's stable finiteness conjecture},
author = {Federico Berlai},
journal= {arXiv preprint arXiv:1501.02893},
year = {2015}
}
Comments
9 pages, no figures