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FREE GROUPS FROM FIELDS

Published online by Cambridge University Press:  01 April 1997

STEPHEN D. COHEN  and
A. M. W. GLASS
STEPHEN D. COHEN
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW, Scotland
A. M. W. GLASS
Affiliation:
Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, Ohio 43403-0221 USA
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Abstract

In the nineteenth century, field theory brilliantly resolved a number of questions that had taxed mathematicians for centuries; for example, ‘The circle cannot be squared’ by straight edge and compass, and solving polynomial equations by radicals is not always possible. These successes have continued to be held up as superb examples of the power of mathematical thought, and are demonstrated at an undergraduate level. The purpose of this article is to provide another such natural example which leads to a concrete realisation of the free group on 2 generators.

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 55 , Issue 2 , April 1997 , pp. 309 - 319
Copyright
The London Mathematical Society 1997

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