Geodesic
Hilbert’s fifth problem for local groups
Isaac Goldbring1
1University of Illinois<br/>Department of Mathematics<br/>1409 W. Green Street<br/>Urbana, IL 61801<br/>and <br/>University of California, Los Angeles<br/>Department of Mathematics<br/>520 Portola Plaza, Box 951555<br/>Los Angeles CA 90095-1555
Annals of mathematics, Tome 172 (2010) no. 2, pp. 1269-1314
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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.

DOI : 10.4007/annals.2010.172.1269

Isaac Goldbring  1

1 University of Illinois<br/>Department of Mathematics<br/>1409 W. Green Street<br/>Urbana, IL 61801<br/>and <br/>University of California, Los Angeles<br/>Department of Mathematics<br/>520 Portola Plaza, Box 951555<br/>Los Angeles CA 90095-1555 
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     title = {Hilbert{\textquoteright}s fifth problem for local groups},
     journal = {Annals of mathematics},
     pages = {1269--1314},
     year = {2010},
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     number = {2},
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     mrnumber = {2680491},
     zbl = {1219.22004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4007/annals.2010.172.1269/}
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Isaac Goldbring. Hilbert’s fifth problem for local groups. Annals of mathematics, Tome 172 (2010) no. 2, pp. 1269-1314. doi: 10.4007/annals.2010.172.1269

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