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Automorphisms of Coxeter groups
Author(s):
Patrick
Bahls
Journal:
Trans. Amer. Math. Soc.
358
(2006),
1781-1796.
MSC (2000):
Primary 20F28, 20F55
Posted:
October 21, 2005
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Abstract:
We compute  for any even Coxeter group whose Coxeter diagram is connected, contains no edges labeled 2, and cannot be separated into more than 2 connected components by removing a single vertex. The description is given explicitly in terms of the given presentation for the Coxeter group and admits an easy characterization of those groups  for which  is finite.
References:
-
- 1.
- Bahls, P., ``Even rigidity in Coxeter groups'', Ph.D. Thesis, Vanderbilt University, 2002.
- 2.
- Bahls, P., ``Strongly rigid even Coxeter groups'', Topology Proceedings 28 (2004) no. 1, 19-54. MR 2105446 (2005i:20063)
- 3.
- Bahls, P., and Mihalik, M., ``Reflection independence in even Coxeter groups'', Geom. Ded. 110 (2005) no. 1, 63-80. MR 2136020
- 4.
- Bahls, P., and Mihalik, M., ``Centralizers of parabolic subgroups of Coxeter groups'', preprint, 2003.
- 5.
- Bourbaki, N., Groupes et Algebres de Lie, Chap. IV-VI, Hermann, Paris, 1981.MR 0647314 (83g:17001)
- 6.
- Charney, R., and Davis, M., ``When is a Coxeter group determined by its system?'', J. London Math. Soc. (2) 61 (2000) no. 2, 441-461.MR 1760693 (2001i:20078)
- 7.
- Franzsen, W., and Howlett, R., ``Automorphisms of Coxeter groups of rank 3'', Proc. Am. Math. Soc. 129 (2001) no. 9, 2607-2616.MR 1838783 (2002c:20060)
- 8.
- Franzsen, W., ``Automorphisms of Coxeter groups of rank 3 with infinite bonds,'' J. Algebra 248 (2002) no. 1, 381-396. MR 1879023 (2003f:20060)
- 9.
- Gilbert, N., ``Presentations of the automorphism group of a free product,'' Proc. London Math. Soc. (3) 54 (1987), 115-140.MR 0872253 (87m:20076)
- 10.
- Howlett, R., Rowley, P., and Taylor, D., ``On outer automorphism groups of Coxeter groups'', Manuscripta Math. 93 (1997) no. 4, 499-513.MR 1465894 (98j:20056)
- 11.
- James, L., ``Complexes and Coxeter groups - operations and outer automorphisms'', J. Algebra 113 (1988) no. 2, 339-345. MR 0929764 (89c:20055)
- 12.
- Levitt, G., ``Automorphisms of hyperbolic groups and graphs of groups'', preprint, 2003.
- 13.
- Lyndon, R., and Schupp, P., Combinatorial Group Theory, Ergebnisse series, vol. 89, Springer, New York, 1977 (reprinted in the Springer Classics in Mathematics Series, 2000). MR 1812024 (2001i:20064)
- 14.
- Mihalik, M., and Tschantz, S., ``Visual decompositions of Coxeter groups'', preprint, 2001.
- 15.
- Mühlherr, B., ``Automorphisms of graph-universal Coxeter groups'', J. Algebra 200 (1998) no. 2, 629-649. MR 1610676 (98m:20048)
- 16.
- Mühlherr, B., and Weidmann, R., ``Rigidity of skew-angled Coxeter groups'', Adv. Geom. 2 (2002) no. 4, 391-415.MR 1941338 (2003h:20073)
- 17.
- Rips, E., and Sela, Z., ``Structure and rigidity in hyperbolic groups I'', Geom. Func. Anal. 4 no. 3 (1994), 337-371.MR 1274119 (96c:20067)
- 18.
- Tits, J., ``Sur le groupe des automorphismes des certains groupes de Coxeter'', J. Algebra 113 (1988) no. 2, 346-357. MR 0929765 (89b:20077)
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Additional Information:
Patrick
Bahls
Affiliation:
Department of Mathematics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801
Email:
pbahls@math.uiuc.edu
DOI:
10.1090/S0002-9947-05-03779-7
PII:
S 0002-9947(05)03779-7
Keywords:
Coxeter group,
group automorphism
Received by editor(s):
May 20, 2003
Received by editor(s) in revised form:
July 9, 2004
Posted:
October 21, 2005
Additional Notes:
The author was supported by an NSF VIGRE postdoctoral grant.
Copyright of article:
Copyright
2005,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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