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Groups of p-deficiency one

Published online by Cambridge University Press:  20 September 2013

ANITHA THILLAISUNDARAM
Affiliation:
Institut für Algebra und Geometrie, Mathematische Fakultät, Otto-von-Guericke-Universität Magdeburg, 39106 Magdeburg, Germany. e-mail: anitha.t@cantab.net
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Abstract

In a previous paper, Button and Thillaisundaram proved that all finitely presented groups of p-deficiency greater than one are p-large. Here we prove that groups with a finite presentation of p-deficiency one possess a finite index subgroup that surjects onto the integers. This implies that these groups do not have Kazhdan's property (T). Additionally, we show that the aforementioned result of Button and Thillaisundaram implies a result of Lackenby.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 2013 

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References

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