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An analogue for semigroups of a group problem of P. Erdös and B. H. Neumann

Published online by Cambridge University Press:  17 April 2009

Luise-Charlotte Kappe ,
John C. Lennox  and
James Wiegold
Luise-Charlotte Kappe
Affiliation:
Department of Math Sciences, Suny at Binghamton, Binghamton, NY 13902–6000, United States of America, e-mail: menger@math.binghamton.edu
John C. Lennox
Affiliation:
School of Mathematics, Cardiff University, Senghennydd Road, PO Box 926, Cardiff, CF24 4YH, Wales, United Kingdom, e-mail: WiegoldJ@Cardiff.ac.uk
James Wiegold
Affiliation:
Green College at the Radcliffe Observatory, Oxford OX2 6HG, United Kingdom, e-mail: jclennox@aol.com
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Abstract

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In response to a question posed by P. Erdös, B. H. Neumann showed that in a group with every subset of pairwise noncommuting elements finite there is a bound on the size of these sets. Recently, H. E. Bell, A. A. Klein and the first author showed that a similar result holds for rings. However in the case of semigroups, finiteness of subsets of pairwise noncommuting elements does not assure the existence of a bound for their size. The largest class of semigroups in which we found Neumann's result valid are cancellative semigroups.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 63 , Issue 1 , February 2001 , pp. 59 - 66
Copyright
Copyright © Australian Mathematical Society 2001

References

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