### A Kirillov theory for divisible nilpotent groups.

A.L. Carey, W. Moran, C.E.M. Pearce (1995)

Mathematische Annalen

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A.L. Carey, W. Moran, C.E.M. Pearce (1995)

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We identify two generalizations of the notion of a finitely generated nilpotent. Thus a nilpotent group G is fgp if G_{p} is fg as p-local group for each p; and G is fg-like if there exists a fg nilpotent group H such that G_{p} ≅ H_{p} for all p. The we have proper set-inclusions:
{fg} ⊂ {fg-like} ⊂ {fgp}.
We examine the extent to which fg-like nilpotent groups satisfy the axioms for...

Hilton, Peter, Militello, Robert (1996)

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This is the second part of a paper about the classification of 2-compact groups. In the first part we set up a general classification procedure and applied it to the simple 2-compact groups of the A-family. In this second part we deal with the other simple Lie groups and with the exotic simple 2-compact group DI(4). We show that all simple 2-compact groups are uniquely N-determined and conclude that all connected 2-compact groups are uniquely N-determined. This means that two connected...

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Carnot groups are distinguished spaces that are rich of structure: they are those Lie groups equipped with a path distance that is invariant by left-translations of the group and admit automorphisms that are dilations with respect to the distance. We present the basic theory of Carnot groups together with several remarks.We consider them as special cases of graded groups and as homogeneous metric spaces.We discuss the regularity of isometries in the general case of Carnot-Carathéodory...

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