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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.


References [Enhancements On Off] (What's this?)

  • [1] C. Chabauty, Limite d'ensembles et géométrie des nombres, Bull. Soc. Math. France 78 (1950), 143-151. MR 12, 479. MR 0038983 (12:479f)
  • [2] J. Dixmier and W. G. Lister, Derivations of nilpotent Lie algebras, Proc. Amer. Math. Soc. 8 (1957), 155-158. MR 18, 659. MR 0083101 (18:659a)
  • [3] D. A. Každan and G. A. Margulis, A proof of Selberg's conjecture, Mat. Sb. 75 (117) (1968), 163-168 = Math. USSR Sb. 4 (1968), 147-152. MR 36 #6535. MR 0223487 (36:6535)
  • [4] G. Leger, Derivations of Lie algebras. III, Duke Math. J. 30 (1963), 637-645. MR 28 #3064. MR 0159848 (28:3064)
  • [5] A. I. Mal'cev, On a class of homogeneous spaces, Izv. Akad. Nauk SSSR Ser. Mat. 13 (1949), 9-32; English transl., Amer. Math. Soc. Transl. (1) 9 (1962), 276-307. MR 10, 507. MR 0028842 (10:507d)
  • [6] H. C. Wang, Topics on totally discontinuous groups, Short Courses in Symmetric Spaces, Dekker, New York, 1972. MR 0414787 (54:2879)

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

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