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On the Lie theory of p-adic analytic groups

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Abstract.

The aim of this paper is to fill a small, but fundamental, gap in the theory of p-adic analytic groups. We illustrate by example that the now standard notion of a uniformly powerful pro-p group is more restrictive than Lazard’s concept of a saturable pro-p group. For instance, the Sylow-pro-p subgroups of many classical groups are saturable, but need not be uniformly powerful. Extending work of Ilani, we obtain a correspondence between subgroups and Lie sublattices of saturable pro-p groups. This leads to applications, for instance, in the subject of subgroup growth.

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  1. Mathematisches Institut, Heinrich-Heine-Universität, 40225, Düsseldorf, Germany

    Benjamin Klopsch

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  1. Benjamin Klopsch
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Correspondence to Benjamin Klopsch.

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Mathematics Subject Classification (2000): 22E20

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Klopsch, B. On the Lie theory of p-adic analytic groups. Math. Z. 249, 713–730 (2005). https://doi.org/10.1007/s00209-004-0717-1

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  • DOI: https://doi.org/10.1007/s00209-004-0717-1

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