Hostname: page-component-7dd5485656-wjfd9 Total loading time: 0 Render date: 2025-10-31T09:50:29.892Z Has data issue: false hasContentIssue false
  • English
  • Français

PROJECTIVE LINEAR GROUPS AS MAXIMAL SYMMETRY GROUPS

Published online by Cambridge University Press:  01 January 2008

ANNA TORSTENSSON
ANNA TORSTENSSON*
Affiliation:
Centre for Mathematical Sciences, Box 118, SE-221 00 Lund, Sweden e-mail: annat@maths.lth.se
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A maximal symmetry group is a group of isomorphisms of a three-dimensional hyperbolic manifold of maximal order in relation to the volume of the manifold. In this paper we determine all maximal symmetry groups of the types PSL(2, q) and PGL(2, q). Depending on the prime p there are one or two such groups with q=pk and k always equals 1, 2 or 4.

Keywords

20B2520G40

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 50 , Issue 1 , January 2008 , pp. 83 - 96
Copyright
Copyright © Glasgow Mathematical Journal Trust 2008

References

REFERENCES

1.Marston, D. E., Conder Gaven, J.Martin and Anna Torstensson, Maximal symmetry groups of hyperbolic 3-manifolds, New Zealand J. Math. 35 (2006), 37–62.Google Scholar
2.Gehring, F. W. and Martin, G. J., Minimal co-volume lattices, i: spherical points of a Kleinian group, to appear.Google Scholar
3.Gehring, F. W. and Martin, G. J., (p, q, r)-Kleinian groups and the Margulis constant, to appear.Google Scholar
4.Gehring, F. W. and Martin, G. J., Precisely invariant collars and the volume of hyperbolic 3-folds, J. Differential Geom. 49 (3) (1998), 411–435.CrossRefGoogle Scholar
5.Gehring, F. W. and Martin, G. J., The volume of hyperbolic 3-folds with p-torsion, p\ge6, Quart. J. Math. Oxford Ser. (2), 50 (1999), 1–12.CrossRefGoogle Scholar
6.Long, D. D. and Reid, A. W., Simple quotients of hyperbolic 3-manifold groups, Proc. Amer. Math. Soc. 126 (3) (1998), 877–880.CrossRefGoogle Scholar
7.Macbeath, A. M., Generators of the linear fractional groups, in Number theory (Proc. Sympos. Pure Math., Vol. XII, Houston, Tex., 1967) (Amer. Math. Soc., Providence, R.I., 1969), 14–32.CrossRefGoogle Scholar
8.Colin, Maclachlan and Alan, W. Reid, The arithmetic of hyperbolic 3-manifolds (Springer-Verlag, 2003).CrossRefGoogle Scholar
9.Marshall, T. H. and Martin, G. J., Minimal co-volume lattices, ii: simple torsion in Kleinian groups, to appear.Google Scholar
10.Bernard, Maskit, Kleinian groups (Springer-Verlag, 1988).CrossRefGoogle Scholar
11.Luisa, Paoluzzi, PSL (2, q) quotients of some hyperbolic tetrahedral and Coxeter groups, Comm. Algebra 26 (3) (1998), 759–778.Google Scholar
12.Hsien, Chung Wang, Topics on totally discontinuous groups, in Symmetric spaces (Short Courses, Washington Univ., St. Louis, Mo., 1969–1970), Pure and Appl. Math., Vol. 8. (Dekker, New York, 1972), 459–487.Google Scholar