Characteristic random subgroups of geometric groups and free abelian groups of infinite rank

Bowen, Lewis; Grigorchuk, Rostislav; Kravchenko, Rostyslav

doi:10.1090/tran/6695

Characteristic random subgroups of geometric groups and free abelian groups of infinite rank
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by Lewis Bowen, Rostislav Grigorchuk and Rostyslav Kravchenko PDF

Trans. Amer. Math. Soc. 369 (2017), 755-781 Request permission

Abstract:

We show that if $G$ is a non-elementary word hyperbolic group, mapping class group of a hyperbolic surface or the outer automorphism group of a non-abelian free group, then $G$ has $2^{\aleph _0}$ many non-atomic ergodic invariant random subgroups. If $G$ is a non-abelian free group, then $G$ has $2^{\aleph _0}$ many non-atomic $G$-ergodic characteristic random subgroups. We also provide a complete classification of characteristic random subgroups of free abelian groups of countably infinite rank and elementary $p$-groups of countably infinite rank.

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