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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| 格式: | Journal article |
| 語言: | English |
| 出版: |
Wiley
2021
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| 總結: | 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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