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Proceedings of the American Mathematical Society

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

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Free products in linear groups
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by D. S. Passman PDF
Proc. Amer. Math. Soc. 132 (2004), 37-46 Request permission

Abstract:

Let $R$ be a commutative integral domain of characteristic $0$, and let $G$ be a finite subgroup of $\mathrm {PGL}_n(R)$, the projective general linear group of degree $n$ over $R$. In this note, we show that if $n\geq 2$, then $\mathrm {PGL}_n(R)$ also contains the free product $G*T$, where $T$ is the infinite cyclic group generated by the image of a suitable transvection.
References
  • J. Z. Gonçalves and A. Mandel, Free groups generated by transvections, to appear.
  • Pierre de la Harpe, Topics in geometric group theory, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, 2000. MR 1786869
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Additional Information
  • D. S. Passman
  • Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
  • MR Author ID: 136635
  • Email: passman@math.wisc.edu
  • Received by editor(s): August 26, 2002
  • Published electronically: May 9, 2003
  • Communicated by: Lance W. Small
  • © Copyright 2003 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 132 (2004), 37-46
  • MSC (2000): Primary 20E06, 20H20
  • DOI: https://doi.org/10.1090/S0002-9939-03-07033-3
  • MathSciNet review: 2021246