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The non-existence of a non-abelian nilpotent Lie group with one discrete uniform subgroup up to automorphism.
- Source :
- Archiv der Mathematik; May2012, Vol. 98 Issue 5, p441-447, 7p
- Publication Year :
- 2012
-
Abstract
- Let G be a connected, simply connected nilpotent Lie group and $${\fancyscript{S}(G)}$$ the space of the discrete uniform subgroups of G. In this paper, we give some necessary and sufficient conditions for $${\fancyscript{S}(G)}$$ under which the group G is abelian. In particular, we prove the non-existence of non-abelian nilpotent Lie groups with one discrete uniform subgroup up to automorphism. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 0003889X
- Volume :
- 98
- Issue :
- 5
- Database :
- Complementary Index
- Journal :
- Archiv der Mathematik
- Publication Type :
- Academic Journal
- Accession number :
- 75255400
- Full Text :
- https://doi.org/10.1007/s00013-012-0383-1