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Finite quotients of rings and applications to subgroup separability of linear groups


Author: Emily Hamilton
Journal: Trans. Amer. Math. Soc. 357 (2005), 1995-2006
MSC (2000): Primary 20E26, 57M05
DOI: https://doi.org/10.1090/S0002-9947-04-03580-9
Published electronically: October 7, 2004
MathSciNet review: 2115087
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Abstract: In this paper we apply results from algebraic number theory to subgroup separability of linear groups. We then state applications to subgroup separability of free products with amalgamation of hyperbolic $3$-manifold groups.


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  • 1. E.S. Allman and E. Hamilton, Abelian subgroups of finitely generated Kleinian groups are separable', Bull. London Math. Soc. 31 (1999) 163 - 172. MR 99m:20118
  • 2. R.C. Alperin, `An elementary account of Selberg's Lemma', L'Enseignement Mathematique t.33 (1987) 269 - 273. MR 89f:20051
  • 3. H. Bass, Groups of integral representation type', Pacific Journal of Math. 86, No.1 (1980) 15 - 50. MR 82c:20014
  • 4. H. Bass and J. Morgan (editors), `The Smith Conjecture', (Academic Press, 1984).MR 86i:57002
  • 5. G. Baumslag, `On the residual finiteness of generalized free products of nilpotent groups', Trans. Amer. Math. Soc. (2) 106 (1963) 193 - 209.MR 26:2489
  • 6. A.M. Brunner, R.G. Burns and D. Solitar, `The subgroup separability of free products of two free groups with cyclic amalgamation', Contributions to groups theory, 90 - 115, Contemp. Math., 33, Amer. Math. Soc., Providence, RI, 1984. MR 86e:20033
  • 7. M. Culler and P. Shalen, `Varieties of group representations and splittings of 3-manifolds' Ann. of Math. 117 (1983) 109 - 146. MR 84k:57005
  • 8. M. Hall, `Coset representations in free groups', Trans. Amer. Math. Soc. 67 (1949) 421 - 432. MR 11:322e
  • 9. E. Hamilton, `Abelian subgroup separability of Haken $3$-manifolds and closed hyperbolic $n$-orbifolds', Proc. London Math. Soc. (3) 83 (2001) 626 - 646. MR 2002g:57033
  • 10. E. Hamilton, `Classes of separable two-generator free subgroups of $3$-manifold groups', Topology Appl., 131 (2003) 239 - 254.
  • 11. G.J. Janusz, `Algebraic Number Fields', (Academic Press, 1973). MR 51:3110
  • 12. D.D. Long, `Immersions and embeddings of totally geodesic surfaces', Bull. London Math. Soc. 19 (1987) 481 - 484. MR 89g:57014
  • 13. D.D. Long and G.A. Niblo, `Subgroup separability and $3$-manifold groups', Math. Z. 207 (1991) 209 - 215. MR 92g:20047
  • 14. A.I. Mal'cev, `On homomorphisms to finite groups' American Mathematical Society Translations, Series 2, 119 (1983) 67 - 79.
  • 15. G.A. Niblo, Ph.D. thesis, University of Michigan.
  • 16. L.P. Postnikova and A. Schinzel, `Primitive divisors of the expression $a^n - b^n$ in algebraic number fields', Mat. Sbornik, 75 (1968) 171 - 177 (in Russian), Math. USSR-Sbornik 4 (1968) 153 - 159. MR 36:6378
  • 17. J. Ratcliffe, `Foundations of Hyperbolic Manifolds', (Springer-Verlag, 1994). MR 95j:57011
  • 18. A. Schinzel, `Primitive divisors of the expression $A^n - B^n$ in algebraic number fields', J. Reine Angew. Math., 268/269 (1974) 27 - 33.MR 49:8961
  • 19. P. Scott, `Subgroups of surface groups are almost geometric', J. London Math. Soc. 17 (1978) 555-565. MR 58:12996
  • 20. W.P. Thurston, `The geometry and topology of $3$-manifolds', Mimeographed lecture notes, Princeton University, 1978.

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Additional Information

Emily Hamilton
Affiliation: Department of Mathematics and Computer Science, Emory University, Atlanta, Georgia 30322

DOI: https://doi.org/10.1090/S0002-9947-04-03580-9
Received by editor(s): July 3, 2002
Received by editor(s) in revised form: December 2, 2003
Published electronically: October 7, 2004
Additional Notes: The author was partially supported by NSF Grant DMS 9973317
Article copyright: © Copyright 2004 American Mathematical Society

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