Duke Mathematical Journal
- Duke Math. J.
- Volume 168, Number 12 (2019), 2207-2234.
Stability and invariant random subgroups
Consider endowed with the normalized Hamming metric . A finitely generated group is P-stable if every almost homomorphism (i.e., for every , ) is close to an actual homomorphism . Glebsky and Rivera observed that finite groups are P-stable, while Arzhantseva and Păunescu showed the same for abelian groups and raised many questions, especially about the P-stability of amenable groups. We develop P-stability in general and, in particular, for amenable groups. Our main tool is the theory of invariant random subgroups, which enables us to give a characterization of P-stability among amenable groups and to deduce the stability and instability of various families of amenable groups.
Duke Math. J., Volume 168, Number 12 (2019), 2207-2234.
Received: 5 March 2018
Revised: 15 January 2019
First available in Project Euclid: 14 August 2019
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Becker, Oren; Lubotzky, Alexander; Thom, Andreas. Stability and invariant random subgroups. Duke Math. J. 168 (2019), no. 12, 2207--2234. doi:10.1215/00127094-2019-0024. https://projecteuclid.org/euclid.dmj/1565748248