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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.

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On the distribution of values of certain word maps
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by Michael Larsen and Aner Shalev PDF
Trans. Amer. Math. Soc. 368 (2016), 1647-1661 Request permission

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.
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Additional Information
  • Michael Larsen
  • Affiliation: Department of Mathematics, Indiana University, Bloomington, Indiana 47405
  • MR Author ID: 293592
  • Email: mjlarsen@indiana.edu
  • Aner Shalev
  • Affiliation: Einstein Institute of Mathematics, Hebrew University, Givat Ram, Jerusalem 91904, Israel
  • MR Author ID: 228986
  • ORCID: 0000-0001-9428-2958
  • Email: shalev@math.huji.ac.il
  • 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.
  • © Copyright 2015 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 368 (2016), 1647-1661
  • MSC (2010): Primary 20P05, 20D06
  • DOI: https://doi.org/10.1090/tran/6389
  • MathSciNet review: 3449221