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Groups with one defining relator

Published online by Cambridge University Press:  09 April 2009

Gilbert Baumslag
Gilbert Baumslag
Affiliation:
City University of New York, 33 West 42nd Street, New York City.
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The present day theory of finite groups might be regarded as the outgrowth of the algebraic theory of equations. In much the same way one might consider the modern theory of infinite groups as stemming from late nineteenth century topology. The groups that crop up in topology are of a particularly simple type in that they are both finitely generated and finitely related. This means that every element in such a group can be expressed in terms of a finite number of elements and their inverses and every relation is an algebraic consequence of a finite number of relations between these elements. In other words the legacy of topology to group theory is the estate of finitely presented groups. This talk is concerned with the seemingly simplest of the finitely presented groups, the so-called groups with a single defining relator.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 4 , Issue 4 , November 1964 , pp. 385 - 392
Copyright
Copyright © Australian Mathematical Society 1964

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