Pro-p groups with constant generating number on open subgroups

2010/06/07 by Klopsch, B., Snopce, I.
#20E18 (Primary) 22E20 (Secondary) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1006.1208

Abstract

Let p be a prime. We classify finitely generated pro-p groups G which satisfy d(H) = d(G) for all open subgroups H of G. Here d(H) denotes the minimal number of topological generators for the subgroup H. Within the category of p-adic analytic pro-p groups, this answers a question of Iwasawa.

Related

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• A characterisation of uniform pro-p groups
• Schreier's formula for Prosupersolvable groups
• Virtually free pro-p products
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