Journal of Lie Theory
Vol. 12, No. 1, pp. 305--308 (2002)
The Abelian Subgroup Conjecture: A Counter Example
W. HerfortWolfgang Herfort
University of Technology
Abstract: If an abelian subgroup $A$ of a locally compact group $G$ has the same weigth as $G$, it is termed large (see Hofmann, K. H., and S. A. Morris, Compact groups with large abelian subgroups, Math. Proc. Cambridge Philos. Soc. 133 (2002), to appear). 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 set $X$ of cardinality greater than $\aleph_0$ contains a large abelian subgroup.
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Electronic fulltext finalized on: 30 Oct 2001. This page was last modified: 9 Nov 2001.