Journal of Lie Theory 12 (2002), No. 1, 305--308
Copyright Heldermann Verlag 2002
The Abelian Subgroup Conjecture: A Counter Example
Wolfgang Herfort
Technische Universität, Wien, Austria
If an abelian subgroup A of a locally compact group G has the same weigth as G, it is termed "large" [see K. H. Hofmann and S. A. Morris, "Compact groups with large abelian subgroups", Math. Proc. Cambridge Philos. Soc. 133 (2002) 235--247]. It has been conjectured that every compact group has a large abelian subgroup. In this note we show that no free pro-p group F(X) on a set X of cardinality greater than Aleph0 contains a large abelian subgroup.
[ Fulltext-pdf (116 KB)]