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Groups satisfying Kaplansky's stable finiteness conjecture (1501.02893v1)

Published 13 Jan 2015 in math.GR

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.

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