Free quotients of $SL_2(R[x])$
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- by Sava Krstic and James McCool PDF
- Proc. Amer. Math. Soc. 125 (1997), 1585-1588 Request permission
Abstract:
It is shown that if $R$ is an integral domain which is not a field, and $U_2(R[x])$ is the subgroup of $SL_2(R[x])$ generated by all unipotent elements, then the quotient group $SL_2(R[x])/U_2(R[x])$ has a free quotient of infinite rank.References
- Warren Dicks and M. J. Dunwoody, Groups acting on graphs, Cambridge Studies in Advanced Mathematics, vol. 17, Cambridge University Press, Cambridge, 1989. MR 1001965
- Fritz Grunewald, Jens Mennicke, and Leonid Vaserstein, On the groups $\textrm {SL}_2(\textbf {Z}[x])$ and $\textrm {SL}_2(k[x,y])$, Israel J. Math. 86 (1994), no.Β 1-3, 157β193. MR 1276133, DOI 10.1007/BF02773676
- A. W. Mason, Normal subgroups of $\textrm {SL}_2(k[t])$ with or without free quotients, J. Algebra 150 (1992), no.Β 2, 281β295. MR 1176897, DOI 10.1016/S0021-8693(05)80032-8
- Hirosi Nagao, On $\textrm {GL}(2,\,K[x])$, J. Inst. Polytech. Osaka City Univ. Ser. A 10 (1959), 117β121. MR 114866
- Jean-Pierre Serre, Trees, Springer-Verlag, Berlin-New York, 1980. Translated from the French by John Stillwell. MR 607504, DOI 10.1007/978-3-642-61856-7
Additional Information
- Sava Krstic
- Affiliation: Department of Mathematics, Tufts University, Medford, Massachusetts 02155
- Email: skrstic@diamond.tufts.edu
- James McCool
- Affiliation: Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 1A1
- Email: mccool@math.toronto.edu
- Received by editor(s): October 31, 1995
- Additional Notes: The first author was partially supported by a grant from Science Fund of Serbia.
The second authorβs research was supported by a grant from NSERC Canada. - Communicated by: Ronald M. Solomon
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 1585-1588
- MSC (1991): Primary 20H25, 20E08
- DOI: https://doi.org/10.1090/S0002-9939-97-03809-4
- MathSciNet review: 1376995