On some Λ-analytic pro-p groups
- Cite this article as:
- Lubotzky, A. & Shalev, A. Israel J. Math. (1994) 85: 307. doi:10.1007/BF02758646
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This paper is devoted to the first steps towards a systematic study of pro-p groups which are analytic over a commutative Noetherian local pro-p ring Λ, e.g. Λ=Open image in new window. We restrict our attention to Λ-standard groups, which are pro-p groups arising from a formal group defined over Λ. Under some additional assumptions we show that these groups are of ‘intermediate growth’ in various senses, strictly betweenp-adic analytic pro-p groups and free pro-p groups. This suggests a refinement of Lazard's theory which stresses the dichotomy betweenp-adic analytic pro-p groups and all the others. In the course of the discussion we answer a question posed in [LM1], and settle two conjectures from [Bo].