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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A commutativity criterion for closed subgroups of compact Lie groups.


Author: Joseph A. Wolf
Journal: Proc. Amer. Math. Soc. 27 (1971), 619-622
MSC: Primary 22.50; Secondary 17.00
MathSciNet review: 0277663
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Abstract: Let $ \Gamma $ be a closed subgroup of a compact Lie group $ G$. If the identity component $ {\Gamma _0}$ is commutative, and if the order of $ \Gamma /{\Gamma _0}$ is prime to the order of the Weyl group of $ G$, then it is shown that $ \Gamma $ is commutative. If $ G$ is a classical group this extends a theorem of Burnside on finite linear groups. If $ G$ is exceptional this gives some information on Cayley-Dickson algebras, Jordan algebras and the Cayley protective plane.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0277663-9
PII: S 0002-9939(1971)0277663-9
Keywords: Lie group, closed subgroup, commutative subgroup, Weyl group, linear group, Jordan algebra
Article copyright: © Copyright 1971 American Mathematical Society