Recognising Z(p)[[t]]-analytic pro-p groups by Camina, R, Du Sautoy, M

“…This is a one-way analogue of Lazard's succesful answer to the p-adic version of Hilbert's Fifth Problem. In the course of the proof we define a T-map, a T-uniform group and set up a category equivalence between T-uniform pro-p groups and powerful ℤ p[[t]]-Lie algebras. © 2006 Cambridge Philosophical Society.…”

The structure of approximate groups by Breuillard, E, Green, B, Tao, T

“…These arose in the solution of Hilbert's fifth problem in the 1950s. Applications of our main theorem include a finitary refinement of Gromov's theorem, as well as a generalized Margulis lemma conjectured by Gromov and a result on the virtual nilpotence of the fundamental group of Ricci almost nonnegatively curved manifolds.…”