Positive rank gradient and p-largeness for groups defined by presentations with p-deficiency less than or equal to one

Abstract

It is an immediate consequence of the results by Yiftach and Schlage-Puchta that a presentation with p-deficiency greater than one defines a group with positive rank gradient. By results of Button and Thillaisundaram, a finite presentation with p-deficiency greater than one defines a p-large group. Both Yiftach/Schlage-Puchta and Thillaisundaram extended these results to the p-deficiency one case. In this paper we consider the case when the presentation has p-deficiency less than or equal to one.

14 pages

References in corpus (4)

• Rank gradient and torsion groups
• On $p$-deficiency in groups
• Residual Deficiency
• Groups of p-deficiency one

Cited by in corpus (1)

• Rank gradient and p-gradient of amalgamated free products and HNN extensions