Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Characteristic random subgroups of geometric groups and free abelian groups of infinite rank
HTML articles powered by AMS MathViewer

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
Similar Articles
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