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The non-existence of a non-abelian nilpotent Lie group with one discrete uniform subgroup up to automorphism.

Authors :
Hamrouni, Hatem
Souissi, Salah
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