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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Free products in linear groups


Author: D. S. Passman
Journal: Proc. Amer. Math. Soc. 132 (2004), 37-46
MSC (2000): Primary 20E06, 20H20
Published electronically: May 9, 2003
MathSciNet review: 2021246
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Abstract | References | Similar Articles | Additional Information

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

  • [GM] J. Z. Gonçalves and A. Mandel, Free groups generated by transvections, to appear.
  • [H] Pierre de la Harpe, Topics in geometric group theory, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, IL, 2000. MR 1786869 (2001i:20081)

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Additional Information

D. S. Passman
Affiliation: Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
Email: passman@math.wisc.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07033-3
PII: S 0002-9939(03)07033-3
Received by editor(s): August 26, 2002
Published electronically: May 9, 2003
Communicated by: Lance W. Small
Article copyright: © Copyright 2003 American Mathematical Society