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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Toral subgroups lying in the centralizer of the group of units


Author: R. P. Hunter
Journal: Proc. Amer. Math. Soc. 79 (1980), 113-121
MSC: Primary 22A15
DOI: https://doi.org/10.1090/S0002-9939-1980-0560596-3
MathSciNet review: 560596
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Abstract: Let S be a compact connected finite dimensional monoid whose group of units G is a compact connected Lie group. Then there is an open set W about the unit element such that any compact subgroup within W has dimension at most $ \dim S - \dim G - 1$ and if any toral subgroup achieves this dimension then that toral subgroup lies in the centralizer of G. Two applications are given, one to embeddings of irreducible monoids into S.


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DOI: https://doi.org/10.1090/S0002-9939-1980-0560596-3
Article copyright: © Copyright 1980 American Mathematical Society