Abstract
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.
Citation
Oren Becker. Alexander Lubotzky. Andreas Thom. "Stability and invariant random subgroups." Duke Math. J. 168 (12) 2207 - 2234, 1 September 2019. https://doi.org/10.1215/00127094-2019-0024
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