Submission date: 17 September 2022

Abstract:

Solves Problem 1 in `Finite axiomatizability for profinite groups', Proc. London Math. Soc.(3) 123, (2021).
A soluble pro-p group of finite rank is finitely axiomatizable in the class of all profinite groups if and only if for each open subgroup H, the image of Z(H) in the abelianization of H is finite, subject to some suitable hypothesis of finite presentability.

Mathematics Subject Classification: 20A15, 20E18

Keywords and phrases:

Full text arXiv 2209.08279: pdf, ps.