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 GolodShafarevich, and has a finite index subgroup which is GolodShafarevich for the remaining primes. We also generalize a result of Grigorchuk on Coxeter groups to odd primes. © 2011 World Scientific Publishing Company.