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On semigroups defined by Coxeter-type presentations

Published online by Cambridge University Press:  14 November 2011

C. M. Campbell ,
E. F. Robertson ,
N. Ruškuc  and
R. M. Thomas
C. M. Campbell
Affiliation:
Mathematical Institute, University of St Andrews, St Andrews KYI6 9SS, Scotland, U.K
E. F. Robertson
Affiliation:
Mathematical Institute, University of St Andrews, St Andrews KYI6 9SS, Scotland, U.K
N. Ruškuc
Affiliation:
Mathematical Institute, University of St Andrews, St Andrews KYI6 9SS, Scotland, U.K
R. M. Thomas
Affiliation:
Department of Mathematics and Computer Science, University of Leicester, Leicester LEI 7RH, England, U.K
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Extract

Presentations of Coxeter type are defined for semigroups. Minimal right ideals of a semigroup defined by such a presentation are proved to be isomorphic to the group with the same presentation. A necessary and sufficient condition for these semigroups to be finite is found. The structure of semigroups defined by Coxeter-type presentations for the symmetric and alternating groups is examined in detail.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 125 , Issue 5 , 1995 , pp. 1063 - 1075
Copyright
Copyright © Royal Society of Edinburgh 1995

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References

1Campbell, C. M., Robertson, E. F., Ruškuc, N. and Thomas, R. M.. Semigroup and group presentations. Bull. London Math. Soc. 27 (1995), 46–50.CrossRefGoogle Scholar
2Coxeter, H. S. M.. The complete enumeration of finite groups of the form . J. London Math. Soc. 10(1935), 21–5.CrossRefGoogle Scholar
3Coxeter, H. S. M. and Moser, W. O. J.. Generators and Relations for Discrete Groups (Berlin: Springer, 1980).CrossRefGoogle Scholar
4Moore, E. H.. Concerning the abstract groups of order k! (k!/2),…. Proc. London Math. Soc. (1) 28 (1897), 357–66.Google Scholar
5Ruškuc, N.. Semigroup Presentations (Ph.D. Thesis, University of St Andrews, 1995).Google Scholar
6Soicher, L. H.. Presentations of some finite groups with applications to the O'Nan simple group. J. Algebra 108 (1987), 310–16.CrossRefGoogle Scholar
7Soicher, L. H.. Presentations for Conway's group Co 1. Math. Proc. Cambridge Philos. Soc. 102 (1987), 1–3CrossRefGoogle Scholar