## 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.## References

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## Additional Information

**Lewis Bowen**- Affiliation: Department of Mathematics, University of Texas, Austin, Texas 78712
- MR Author ID: 671629
- Email: lpbowen@math.utexas.edu
**Rostislav Grigorchuk**- Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
- MR Author ID: 193739
- Email: grigorch@math.tamu.edu
**Rostyslav Kravchenko**- Affiliation: Department of Mathematics, University of Chicago, Chicago, Illinois 60637
- Address at time of publication: Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, Illinois 60208
- Email: rkchenko@math.northwestern.edu
- Received by editor(s): May 19, 2014
- Received by editor(s) in revised form: January 20, 2015
- Published electronically: May 6, 2016
- Additional Notes: The first author was supported by NSF grant DMS-0968762 and NSF CAREER Award DMS-0954606

The second author was supported by NSF grant DMS-1207699 - © Copyright 2016 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**369**(2017), 755-781 - MSC (2010): Primary 20K20, 20K27, 20P05, 20E07
- DOI: https://doi.org/10.1090/tran/6695
- MathSciNet review: 3572253