Characterization of p-adic analytic groups in terms of wreath products

Aner Shalev*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


We show that a finitely generated pro-p group is p-adic analytic (i.e., can be given the structure of a Lie group over Qp) if and only if it does not involve arbitrarily large wreath products of the form Cp wr Cpn. This result, whose proof applies Zelmanov's recent solution to the restricted Burnside problem, is in fact equivalent to Zelmanov's Theorem.

Original languageAmerican English
Pages (from-to)204-208
Number of pages5
JournalJournal of Algebra
Issue number1
StatePublished - Jan 1992
Externally publishedYes


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