Applications of p-deficiency and p-largeness

J. O. Button; A. Thillaisundaram

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arXiv · 1007.2845

Applications of p-deficiency and p-largeness

J. O. Button·A. Thillaisundaram

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Abstract

We use Schlage-Puchta's concept of p-deficiency and Lackenby's property of p-largeness to show that a group having a finite presentation with p-deficiency greater than 1 is large, which implies that Schlage-Puchta's infinite finitely generated p-groups are not finitely presented. We also show that for all primes p at least 7, any group having a presentation of p-deficiency greater than 1 is Golod-Shafarevich, and has a finite index subgroup which is Golod-Shafarevich for the remaining primes. We also generalise a result of Grigorchuk on Coxeter groups to odd primes.

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BibTeX RIS

J. O. Button, A. Thillaisundaram. 2010-07-16. Applications of p-deficiency and p-largeness. https://arxiv.org/abs/1007.2845

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