Finite axiomatizability for profinite groups

Author: 

Nies, A
Segal, D
Tent, K

Publication Date: 

24 August 2021

Journal: 

Proceedings of the London Mathematical Society

Last Updated: 

2021-10-21T12:27:45.587+01:00

DOI: 

10.1112/plms.12420

abstract: 

A group is finitely axiomatizable (FA) in a class 𝒞 if it can be determined up to isomorphism within 𝒞 by a sentence in the first-order language of group theory. We show that profinite groups of various kinds are FA in the class of profinite groups, or in the class of pro- 𝑝 groups for some prime 𝑝 . Both algebraic and model-theoretic methods are developed for the purpose. Reasons why certain groups cannot be FA are also discussed.

Symplectic id: 

1185201

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article