Hilbert's Fifth Problem for Local Groups

By Isaac Goldbring. 2007

50 citations recorded by the source corpus.

We solve Hilbert's fifth problem for local groups: every locally euclidean local group is locally isomorphic to a Lie group. Jacoby claimed a proof of this in 1957, but this proof is seriously flawed. We use methods from nonstandard analysis and model our solution after a treatment of Hilbert's fifth problem for global groups by Hirschfeld.

Subfields: Mathematical Physics, Theoretical Computer Science, Philosophy

View Paper: https://www.semanticscholar.org/paper/5d22e391feeb6cc4e6a0cd84f211ce597485c676

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

1. Terence Tao
2. Ben Joseph Green
3. Emmanuel Breuillard
4. Ehud Hrushovski
5. Van H. Vu
6. Zihua Guo
7. D. Tataru
8. Carlos E. Kenig

In Theoretical Computer Science

1. Ben Joseph Green
2. Ehud Hrushovski
3. Emmanuel Breuillard
4. Terence Tao

In Philosophy

1. Ben Joseph Green
2. Ehud Hrushovski
3. Emmanuel Breuillard
4. Terence Tao

Citations in the corpus

• Stable group theory and approximate subgroups (2009, background): “Gromov’s theorem [16] on finitely generated groups of polynomial growth fits into this framework, takingX to be a ball of size 2n in the Cayley graph, for large n; thenX is a 2d-approximate subgroup, where d is the growth exponent.”
• The structure of approximate groups (2011, methodology): “We also thank I. Goldbring and L. van den Dries for showing us a preliminary version of their notes on Hilbert’s fifth problem and its local versions, and J. Lott for help with the references.”