$p$-subgroups of compact Lie groups and torsion of infinite height in $H^{\ast } (BG)$
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- by Mark Feshbach
- Trans. Amer. Math. Soc. 259 (1980), 227-233
- DOI: https://doi.org/10.1090/S0002-9947-1980-0561834-8
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Abstract:
The relation between elementary abelian p-subgroups of a connected compact Lie group G and the existence of p-torsion in ${H^ {\ast } }(G)$ has been known for some time [B-S]. In this paper we prove that if G is any compact Lie group then ${H^ {\ast } }(BG)$ contains p-torsion of infinite height iff G contains an elementary abelian p-group not contained in a maximal torus. The hard direction is proven using the double coset theorem for the transfer. A third equivalent condition is also given.References
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Bibliographic Information
- © Copyright 1980 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 259 (1980), 227-233
- MSC: Primary 55R40
- DOI: https://doi.org/10.1090/S0002-9947-1980-0561834-8
- MathSciNet review: 561834