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A class of one-relator groups with centre

Published online by Cambridge University Press:  17 April 2009

James McCool
James McCool
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Ontario, CanadaM5S 1A1
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Abstract

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Let the group H have presentation where m ≥ 3, pi ≥ 2 and (pi, pj) = 1 if i ≠ j. We show that H is a one-relator group precisely if H can be obtained from a suitable group 〈a, b; ap = bp〉 by repeated applications of a (two-stage) procedure consisting of applying central Nielsen transformations followed by adjoining a root of a generator. We conjecture that any one-relator group G with non-trivial centre and G/G′ not free abelian of rank two can be obtained in the same way from a suitable group 〈a, b; ap = bp〉.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 44 , Issue 2 , October 1991 , pp. 245 - 252
Copyright
Copyright © Australian Mathematical Society 1991

References

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