2024
DOI: 10.2140/pjm.2024.328.255
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Finite axiomatizability of the rank and the dimension of a pro-π group

Martina Conte,
Benjamin Klopsch

Abstract: The Prüfer rank rk(G) of a profinite group G is the supremum, across all open subgroups H of G, of the minimal number of generators d(H). It is known that, for any given prime p, a profinite group G admits the structure of a p-adic analytic group if and only if G is virtually a prop group of finite rank. The dimension dim G of a p-adic analytic profinite group G is the analytic dimension of G as a p-adic manifold; it is known that dim G coincides with the rank rk(U) of any uniformly powerful open prop subgroup… Show more

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