Hilbert’s fifth problem for local groups


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.


Isaac Goldbring

University of Illinois
Department of Mathematics
1409 W. Green Street
Urbana, IL 61801
University of California, Los Angeles
Department of Mathematics
520 Portola Plaza, Box 951555
Los Angeles CA 90095-1555