Free quotients of
Abstract: It is shown that if is an integral domain which is not a field, and is the subgroup of generated by all unipotent elements, then the quotient group has a free quotient of infinite rank.
- 1. Warren Dicks and M. J. Dunwoody, Groups acting on graphs, Cambridge Studies in Advanced Mathematics, vol. 17, Cambridge University Press, Cambridge, 1989. MR 1001965
- 2. Fritz Grunewald, Jens Mennicke, and Leonid Vaserstein, On the groups 𝑆𝐿₂(𝑍[𝑥]) and 𝑆𝐿₂(𝑘[𝑥,𝑦]), Israel J. Math. 86 (1994), no. 1-3, 157–193. MR 1276133, 10.1007/BF02773676
- 3. A. W. Mason, Normal subgroups of 𝑆𝐿₂(𝑘[𝑡]) with or without free quotients, J. Algebra 150 (1992), no. 2, 281–295. MR 1176897, 10.1016/S0021-8693(05)80032-8
- 4. Hirosi Nagao, On 𝐺𝐿(2,𝐾[𝑥]), J. Inst. Polytech. Osaka City Univ. Ser. A 10 (1959), 117–121. MR 0114866
- 5. Jean-Pierre Serre, Trees, Springer-Verlag, Berlin-New York, 1980. Translated from the French by John Stillwell. MR 607504
- W. Dicks and M. J. Dunwoody, Groups acting on graphs, Cambridge University Press, 1989. MR 91b:20001
- F. Grunewald, J. Mennicke and L. Vaserstein, On the groups and , Israel Jour. of Math. 88 (1994), 157-193. MR 95h:20061
- A. W. Mason, Normal subgroups of with or without free quotients, Jour. of Algebra 150 (1992), 281-295. MR 93h:20056
- H. Nagao, On , Jour. Poly. Osaka Univ. 10 (1959), 117-121. MR 22:5684
- J. P. Serre, Trees, Springer-Verlag, New York, 1980. MR 82c:20083
Affiliation: Department of Mathematics, Tufts University, Medford, Massachusetts 02155
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