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Applications of Fox's derivation in determining the generators of a group

Published online by Cambridge University Press:  17 April 2009

Wan Lin
Wan Lin
Affiliation:
Department of Mathematics, University of Manitoba, Winnipeg, Manitoba R3T 2N2, Canada, e-mail: umlin010@cc.umanitoba.ca
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Abstract

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We give a necessary and sufficient condition for a set of elements to be a generating set of a quotient group F/N, where F is the free group of rank n and N is a normal subgroup of F. Birman's Inverse Function Theorem is a corollary of our criterion. As an application of this criterion, we give necessary and sufficient conditions for a set of elements of the Burnside group B (n,p) of exponent p and rank n to be a generating set.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 61 , Issue 1 , February 2000 , pp. 27 - 32
Copyright
Copyright © Australian Mathematical Society 2000

References

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