Arbitrary p-Gradient Values

2012/07/19 by Nathaniel Pappas, Pappas, Nathaniel
Mathematics · #20E15 #20E18 #20F69 #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:20E15 #msc:20E18 #msc:20F69

paper · pdf · doi:10.48550/arxiv.1207.4650

20 pages

arxiv created 2013/01/19 · arxiv updated 2013/01/22

Abstract

For any prime number p and any positive real number α, we construct a finitely generated group Γ with p-gradient equal to α. This construction is used to show that there exist uncountably many pairwise non-commensurable groups that are finitely generated, infinite, torsion, non-amenable, and residually-p.

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