Probabilistic finiteness properties for profinite groups

2019/07/11 by Cook, Ged Corob, Vannacci, Matteo
#20C20 #20C25 #20E18 #20J05 #20J06 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1907.05063

Abstract

We introduce various probablistic finiteness conditions for profinite groups related to positive finite generation (PFG). We investigate completed group rings which are PFG as modules, and use this to answer a question of Kionke and the second author on positively finitely related groups. Using the theory of projective covers, we define and characterise a probabilistic version of the FP_n property for profinite groups, called PFP_n. Finally, we prove how these conditions are related to previously defined finiteness conditions and each other.

Related

• Probabilistic properties of profinite groups
• Rationality of the probabilistic zeta function of finitely generated\n profinite groups
• Counting irreducible modules for profinite groups
• Finiteness properties of profinite groups
• A finiteness condition on the coefficients of the probabilistic zeta function