Hilbert's Fifth Problem for Local Groups

2007/08/28 by Isaac Goldbring, Goldbring, Isaac
Mathematics · #22E05 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Finite Group Theory Research #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.0708.3871

openalex publication_date 2007/08/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Related

• Regularity and nearness theorems for families of local Lie groups
• Globalizing locally compact local groups
• Applications of Lie ring methods to group theory
• Local Hilbert--Schmidt stability
• Lie groups locally isomorphic to generalized Heisenberg groups