Dan Segal, Aner Shalev
Abstract
We characterise the profinite groups with polynomial subgroup growth. We deduce that the property PSG is extension-closed in the category of all groups, and subgroup-closed in the category of finitely generated profinite groups.
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We characterise the profinite groups with polynomial subgroup growth. We deduce that the property PSG is extension-closed in the category of all groups, and subgroup-closed in the category of finitely generated profinite groups.
Key concepts: Profinite group, Mathematics, Extension (predicate logic), Normal subgroup, Finitely-generated abelian group, Polynomial, Index of a subgroup, Pure mathematics