Finite axiomatizability for profinite groups

Finite axiomatizability for profinite groups

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...

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Detalhes bibliográficos
Principais autores: Nies, A, Segal, D, Tent, K
Formato: Journal article
Idioma:English
Publicado em: Wiley 2021
Descrição
Resumo: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.

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