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Finite quotients of rings and applications to subgroup separability of linear groups
Author(s):
Emily
Hamilton
Journal:
Trans. Amer. Math. Soc.
357
(2005),
1995-2006.
MSC (2000):
Primary 20E26, 57M05
Posted:
October 7, 2004
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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 -manifold groups.
References:
-
- 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
-manifolds and closed hyperbolic -orbifolds', Proc. London Math. Soc. (3) 83 (2001) 626 - 646. MR 2002g:57033 - 10.
- E. Hamilton, `Classes of separable two-generator free subgroups of
-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
-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
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
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
-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:
10.1090/S0002-9947-04-03580-9
PII:
S 0002-9947(04)03580-9
Received by editor(s):
July 3, 2002
Received by editor(s) in revised form:
December 2, 2003
Posted:
October 7, 2004
Additional Notes:
The author was partially supported by NSF Grant DMS 9973317
Copyright of article:
Copyright
2004,
American Mathematical Society
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