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Free quotients of $SL_2(R[x])$

Authors: Sava Krstic and James McCool
Journal: Proc. Amer. Math. Soc. 125 (1997), 1585-1588
MSC (1991): Primary 20H25, 20E08
MathSciNet review: 1376995
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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 [Enhancements On Off] (What's this?)

  • 1. W. Dicks and M. J. Dunwoody, Groups acting on graphs, Cambridge University Press, 1989. MR 91b:20001
  • 2. F. Grunewald, J. Mennicke and L. Vaserstein, On the groups $SL_2(\mathbf Z[x])$ and $SL_2(k[x,y])$, Israel Jour. of Math. 88 (1994), 157-193. MR 95h:20061
  • 3. A. W. Mason, Normal subgroups of $SL_2(k[t])$ with or without free quotients, Jour. of Algebra 150 (1992), 281-295. MR 93h:20056
  • 4. H. Nagao, On $GL(2,K[x])$, Jour. Poly. Osaka Univ. 10 (1959), 117-121. MR 22:5684
  • 5. J. P. Serre, Trees, Springer-Verlag, New York, 1980. MR 82c:20083

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Additional Information

Sava Krstic
Affiliation: Department of Mathematics, Tufts University, Medford, Massachusetts 02155

James McCool
Affiliation: Department of Mathematics, University of Toronto, Toronto, Ontario, Canada M5S 1A1

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 author’s research was supported by a grant from NSERC Canada.
Communicated by: Ronald M. Solomon
Article copyright: © Copyright 1997 American Mathematical Society

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