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
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