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GENERATING THE MÖBIUS GROUP WITH INVOLUTION CONJUGACY CLASSES.
- Source :
-
Proceedings of the American Mathematical Society . Nov2012, Vol. 140 Issue 11, p4011-4016. 6p. - Publication Year :
- 2012
-
Abstract
- A k-involution is an involution with a fixed point set of codimension k. The conjugacy class of such an involution, denoted Sk, generates Möb(n)(the group of isometries of hyperbolic n-space) if k is odd and its orientation-preserving subgroup if k is even. In this paper, we supply effective lower and upper bounds for the Sk word length of Möb(n) if k is odd and the Sk word length of Möb+(n) if k is even. As a consequence, for a fixed codimension k, the length of Möb+(n) with respect to Sk, k even, grows linearly with n, with the same statement holding for Möb(n) in the odd case. Moreover, the percentage of involution conjugacy classes for which Möb+(n) has length two approaches zero as n approaches infinity. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 140
- Issue :
- 11
- Database :
- Academic Search Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 77889181
- Full Text :
- https://doi.org/10.1090/S0002-9939-2012-11253-5