A Krull Schmidt theorem for small profinite groups

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• Nikolay Nikolov (University of Oxford)
• Thursday 31 July 2025, 10:15-11:15
• Seminar Room 1, Newton Institute.

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OGGW01 - Discrete and profinite groups

A profinite group is said to be small if it has only finitely many open subgroups of every given index. We prove that every small profinite group can be decomposed into a direct product of indecomposable profinite groups, and that such a decomposition is unique up to order and isomorphisms of the factors. This is closely related to the property of being cancellable in direct products. In this talk I will discuss our investigations of these properties beyond the class of small profinite groups leading to some open questions. This is joint work with Tamar Bar-On.

This talk is part of the Isaac Newton Institute Seminar Series series.

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