Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-10T21:21:33.096Z Has data issue: false hasContentIssue false
  • English
  • Français

Regular maps with small parameters

Part of: Graph theory Low-dimensional topology Special aspects of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

Marston Conder
Marston Conder
Affiliation:
Department of Mathematics and Statistics, University of Auckland, Private Bag 92019, Auckland, New Zealand
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.

Regular maps of type {p, q}r and the associated groups Gp,q,r are considered for small values for p, q and r. In particular, it is shown that the groups G4,6,6 and G5,5,6 are Abelian-by-infinite, and there are infinitely many regular maps of each of the types {4, 6}6, {5, 5}6, {5, 6}6 and {6, 6}6.

MSC classification

Secondary: 05C25: Graphs and abstract algebra (groups, rings, fields, etc.) 20F05: Generators, relations, and presentations 57M15: Relations with graph theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 57 , Issue 1 , August 1994 , pp. 103 - 112
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Cannon, J. J., ‘An introduction to the group theory language CAYLEY’, in: Computational group theory (ed. Atkinson, M.) (Academic Press, SanDiego, 1984) pp. 145–183Google Scholar
[2]Conder, M. D. E., ‘On the group G 6,6,6,, Quart. J. Math. Oxford Ser. (2) 39 (1988), 175–183.CrossRefGoogle Scholar
[3]Coxeter, H. S. M., ‘The abstract groups Gm,n,p,’, Trans. Amer. Math. Soc. 45 (1939), 73–150.Google Scholar
[4]Coxeter, H. S. M. and Moser, W. O. J., Generators and relations for discrete groups, 4th edition (Springer, Berlin, 1980).CrossRefGoogle Scholar
[5]Schönert, M. et al. GAP: Groups, algorithms and programming, Lehrstuhl D für Mathematik, RWTH Aachen (Aachen, 1992).Google Scholar
[6]Wilson, S. E., ‘Cantankerous maps and rotary embeddings of K n’, J. Combin. Theory Ser. B 47 (1989), 262–273.Google Scholar