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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

$ p$-subgroups of compact Lie groups and torsion of infinite height in $ H\sp{\ast} (BG)$


Author: Mark Feshbach
Journal: Trans. Amer. Math. Soc. 259 (1980), 227-233
MSC: Primary 55R40
MathSciNet review: 561834
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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.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1980-0561834-8
PII: S 0002-9947(1980)0561834-8
Keywords: Double coset formula, elementary abelian p-groups, torsion of infinite height, classifying space, transfer, compact Lie group
Article copyright: © Copyright 1980 American Mathematical Society