On one-relator quotients of the modular group

Conder, Marston, Havas, George and Newman, M. F. (2011). On one-relator quotients of the modular group. In: C. M. Campbell, M. R. Quick, E. F. Robertson, C. M. Roney-Dougal, G. C. Smith and G. Traustason, Groups St Andrews 2009 in Bath, Volume 1. Groups St Andrews 2009 in Bath, Bath, United Kingdom, (183-197). 1-15 August 2009.

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Author Conder, Marston
Havas, George
Newman, M. F.
Title of paper On one-relator quotients of the modular group
Conference name Groups St Andrews 2009 in Bath
Conference location Bath, United Kingdom
Conference dates 1-15 August 2009
Proceedings title Groups St Andrews 2009 in Bath, Volume 1
Place of Publication Cambridge, United Kingdom
Publisher Cambridge University Press
Publication Year 2011
Sub-type Fully published paper
ISBN 9780521279031
Editor C. M. Campbell
M. R. Quick
E. F. Robertson
C. M. Roney-Dougal
G. C. Smith
G. Traustason
Start page 183
End page 197
Total pages 15
Collection year 2012
Language eng
Abstract/Summary We investigate the modular group as a finitely presented group. It has a large collection of interesting quotients. In 1987 Conder substantially identified the one-relator quotients of the modular group which are defined using representatives of the 300 inequivalent extra relators with length up to 24. We study all such quotients where the extra relator has length up to 36. Up to equivalence, there are 8296 more presentations. We confirm Conder's results and we determine the order of all except five of the quotients. Once we find the order of a finite quotient it is easy to determine detailed structural information about the group. The presentations of the groups whose order we have not been able to determine provide interesting challenge problems. Our study of one-relator quotients of the modular group is 'in the small', that is, with a short extra relator. We briefly compare and contrast our results with generic results.
Q-Index Code E1
Q-Index Status Confirmed Code
Institutional Status UQ
Additional Notes Published in the London Mathematical Society Lecture Notes Series: 387

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Created: Thu, 20 Oct 2011, 22:13:06 EST by Associate Professor George Havas on behalf of School of Information Technol and Elec Engineering