Small neighborhoods of the identity of a real nilpotent group

Polek, L. P.

doi:10.1090/S0002-9939-1974-0340476-6

Small neighborhoods of the identity of a real nilpotent group
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by L. P. Polek PDF

Proc. Amer. Math. Soc. 42 (1974), 627-630 Request permission

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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