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Proceedings of the American Mathematical Society

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

 

 

On relatively free subsets of Lie groups


Author: Bernard R. Gelbaum
Journal: Proc. Amer. Math. Soc. 58 (1976), 301-305
MSC: Primary 22E15
DOI: https://doi.org/10.1090/S0002-9939-1976-0412343-2
MathSciNet review: 0412343
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Abstract: In an arbitrary neighborhood $ U$ of the identity $ e$ of a connected Lie group there is a subset $ S$ of cardinality $ \mathfrak{c}$ and relatively free , i.e., the only nontrivial equations $ x_1^{{\varepsilon _1}}x_2^{{\varepsilon _2}} \cdots x_n^{{\varepsilon _n}} = e,{\varepsilon _i} = \pm 1$, satisfied by substitution for distinct symbols among the $ {x_i}$ distinct elements of $ S$ are equations that are identities throughout $ G$.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0412343-2
Keywords: Free topological groups, Lie groups and (relatively) free subsets thereof
Article copyright: © Copyright 1976 American Mathematical Society