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Proceedings of the American Mathematical Society

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

 

 

Small neighborhoods of the identity of a real nilpotent group


Author: L. P. Polek
Journal: Proc. Amer. Math. Soc. 42 (1974), 627-630
MSC: Primary 22E25
DOI: https://doi.org/10.1090/S0002-9939-1974-0340476-6
MathSciNet review: 0340476
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Abstract: It is shown that if G is a real nilpotent group of type D, then for every neighborhood U of the identity in G there is a discrete cocompact subgroup $ {\Gamma _U}$ of G such that for every $ \varphi \in {\operatorname{Aut}}(G),\varphi {\Gamma _U}$ and U have more elements in common than just the identity.

This result is exactly the opposite of what is true when G is a semisimple Lie group.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0340476-6
Article copyright: © Copyright 1974 American Mathematical Society