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

Aner Shalev

doi:10.1016/0021-8693(92)90185-O

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

Aner Shalev^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

18 Scopus citations

Abstract

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 Q_p) if and only if it does not involve arbitrarily large wreath products of the form C_p wr C_pⁿ. This result, whose proof applies Zelmanov's recent solution to the restricted Burnside problem, is in fact equivalent to Zelmanov's Theorem.

Original language	English
Pages (from-to)	204-208
Number of pages	5
Journal	Journal of Algebra
Volume	145
Issue number	1
DOIs	https://doi.org/10.1016/0021-8693(92)90185-O
State	Published - Jan 1992
Externally published	Yes

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abstract = "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.",

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AB - 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.

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

Abstract

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