Journal of Lie Theory

no. 1
The Abelian Subgroup Conjecture: A Counter Example
Journal of Lie Theory, Volume 12 (2002) no. 1, pp. 305-308
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.
DOI: 10.5802/jolt.265
Classification: 22C05
Keywords: compact group, Abelian subgroup conjecture, free pro-\(p\) group, \(p\)-Sylow subgroup 
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     author = {W. Herfort},
     title = {The {Abelian} {Subgroup} {Conjecture:} {A} {Counter} {Example}},
     journal = {Journal of Lie Theory},
     pages = {305--308},
     year = {2002},
     volume = {12},
     number = {1},
     doi = {10.5802/jolt.265},
     zbl = {0991.22006},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.265/}
}
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W. Herfort. The Abelian Subgroup Conjecture: A Counter Example. Journal of Lie Theory, Volume 12 (2002) no. 1, pp. 305-308. doi: 10.5802/jolt.265

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