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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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Positive laws in fixed points
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by Pavel Shumyatsky PDF
Trans. Amer. Math. Soc. 356 (2004), 2081-2091 Request permission

Abstract:

Let $A$ be an elementary abelian group of order at least $q^3$ acting on a finite $q’$-group $G$ in such a manner that $C_G(a)$ satisfies a positive law of degree $n$ for any $a\in A^\#$. It is proved that the entire group $G$ satisfies a positive law of degree bounded by a function of $q$ and $n$ only.
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Additional Information
  • Pavel Shumyatsky
  • Affiliation: Department of Mathematics, University of Brasilia, Brasilia-DF, 70910-900 Brazil
  • MR Author ID: 250501
  • Email: pavel@ipe.mat.unb.br
  • Received by editor(s): January 2, 2003
  • Received by editor(s) in revised form: April 15, 2003
  • Published electronically: November 12, 2003
  • Additional Notes: The author was supported by CNPq-Brazil
  • © Copyright 2003 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 356 (2004), 2081-2091
  • MSC (2000): Primary 20D45
  • DOI: https://doi.org/10.1090/S0002-9947-03-03384-1
  • MathSciNet review: 2031054