A profinite analogue of Lasserre's theorem
Group Theory
2023-03-28 v2
Abstract
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.
Keywords
Cite
@article{arxiv.2209.08279,
title = {A profinite analogue of Lasserre's theorem},
author = {Dan Segal},
journal= {arXiv preprint arXiv:2209.08279},
year = {2023}
}
Comments
Solves Problem 1 in `Finite axiomatizability for profinite groups', Proc. London Math. Soc.(3) 123, (2021)