Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

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

Request Permissions   Purchase Content 
 

 

On the distribution of values of certain word maps


Authors: Michael Larsen and Aner Shalev
Journal: Trans. Amer. Math. Soc. 368 (2016), 1647-1661
MSC (2010): Primary 20P05, 20D06
DOI: https://doi.org/10.1090/tran/6389
Published electronically: May 13, 2015
MathSciNet review: 3449221
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We prove that, for any positive integers $ m, n$, the word map $ (x,y) \mapsto x^my^n$ is almost measure preserving on finite simple groups. This extends the case $ m=n=2$ obtained in 2009. Along the way we obtain results of independent interest on fibers of word maps and on character values.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 20P05, 20D06

Retrieve articles in all journals with MSC (2010): 20P05, 20D06


Additional Information

Michael Larsen
Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
Email: mjlarsen@indiana.edu

Aner Shalev
Affiliation: Einstein Institute of Mathematics, Hebrew University, Givat Ram, Jerusalem 91904, Israel
Email: shalev@math.huji.ac.il

DOI: https://doi.org/10.1090/tran/6389
Received by editor(s): August 6, 2013
Received by editor(s) in revised form: December 26, 2013
Published electronically: May 13, 2015
Additional Notes: The first author was partially supported by NSF Grant DMS-1101424. The second author was partially supported by ERC Advanced Grant 247034 and the Vinik Chair in Mathematics. Both authors were partially supported by Binational Science Foundation United States-Israel Grant 2008194.
Article copyright: © Copyright 2015 American Mathematical Society