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ON THE ASPHERICITY OF LENGTH-6 RELATIVE PRESENTATIONS WITH TORSION-FREE COEFFICIENTS

Published online by Cambridge University Press:  04 February 2008

Seong Kun Kim
Seong Kun Kim
Affiliation:
Department of Mathematics, Pusan National University, Pusan 609-735, South Korea ([email protected])
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Abstract

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An interesting result of Ivanov implies that a non-aspherical relative presentation that defines a torsion-free group would provide a potential counterexample to the Kaplansky zero-divisor conjecture. In this point of view, we prove the asphericity of the length-6 relative presentation $\langle H,x: xh_1xh_2xh_3xh_4xh_5xh_6\rangle$, provided that each coefficient is torsion free.

Keywords

Primary 20F05Secondary 57M05asphericityrelative presentationstorsion-free groupszero-divisors
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 51 , Issue 1 , February 2008 , pp. 201 - 214
Copyright
Copyright © Edinburgh Mathematical Society 2008