Uncountably many non-commensurable finitely presented pro-p groups

2015/03/31 by Ilir Snopce, Snopce, Ilir
Mathematics · #20E18 #22E20 #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:20E18 #msc:22E20

paper · pdf · doi:10.48550/arxiv.1504.00027

arxiv created 2015/03/31 · arxiv updated 2015/04/02

Abstract

Let m≥ 3 be a positive integer. We prove that there are uncountably many non-commensurable metabelian uniform pro-p groups of dimension m. Consequently, there are uncountably many non-commensurable finitely presented pro-p groups with minimal number of generators m (and minimal number of relations m \choose 2).

Related

• Higher dimensional algebraic fiberings for pro-p groups
• Weak commutativity for pro-p groups
• Arbitrary p-Gradient Values
• Uncountably many 2-generated just-infinite branch pro-2 groups
• Schreier's formula for Prosupersolvable groups