1Technische Universität, Wien, Austria 2If 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 Aleph 3contains a large abelian subgroup. 4[
Journal of Lie Theory, Tome 12 (2002) no. 1, pp. 305-308
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Wolfgang Herfort. The Abelian Subgroup Conjecture: A Counter Example. Journal of Lie Theory, Tome 12 (2002) no. 1, pp. 305-308. http://geodesic.mathdoc.fr/item/JOLT_2002_12_1_a16/
@article{JOLT_2002_12_1_a16,
author = {Wolfgang Herfort},
title = {The {Abelian} {Subgroup} {Conjecture:} {A} {Counter} {Example}},
journal = {Journal of Lie Theory},
pages = {305--308},
year = {2002},
volume = {12},
number = {1},
url = {http://geodesic.mathdoc.fr/item/JOLT_2002_12_1_a16/}
}
TY - JOUR
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TI - The Abelian Subgroup Conjecture: A Counter Example
JO - Journal of Lie Theory
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%J Journal of Lie Theory
%D 2002
%P 305-308
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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.
