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

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