Groups of p-deficiency one

2011/08/01 by Anitha Thillaisundaram, Thillaisundaram, Anitha
Mathematics · #Geometric and Algebraic Topology #Advanced Topology and Set Theory #Finite Group Theory Research

paper · doi:10.48550/arxiv.1108.0274

Abstract

The main result of [4] is 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 . This implies that these groups do not have Kazhdan's property (T). Additionally, we prove that the main result of [4] implies a result of Lackenby [8].

Related

• Applications of p-deficiency and p-largeness
• Residual Deficiency
• 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
• Rank 1 phenomena for 1-relator and deficiency 1 groups