A commutativity criterion for closed subgroups of compact Lie groups.
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- by Joseph A. Wolf PDF
- Proc. Amer. Math. Soc. 27 (1971), 619-622 Request permission
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.References
- Walter Feit and John G. Thompson, Solvability of groups of odd order, Pacific J. Math. 13 (1963), 775–1029. MR 166261
- Joseph A. Wolf, Spaces of constant curvature, McGraw-Hill Book Co., New York-London-Sydney, 1967. MR 0217740
Additional Information
- © Copyright 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 27 (1971), 619-622
- MSC: Primary 22.50; Secondary 17.00
- DOI: https://doi.org/10.1090/S0002-9939-1971-0277663-9
- MathSciNet review: 0277663