Applications of p-deficiency and p-largeness

2010/07/16 by Button, J. O., Thillaisundaram, A.
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1007.2845

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.

Related

• Groups of p-deficiency one
• Large Groups of Deficiency One
• Positive rank gradient and p-largeness for groups defined by presentations with p-deficiency less than or equal to one
• Detecting large groups
• A characterisation of large finitely presented groups