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- Title
Pro-Lie groups approximable by discrete subgroups.
- Authors
Hamrouni, Hatem; Kadri, Bilel
- Abstract
A locally compact group G is said to be approximable by discrete subgroups if there exists a sequence of discrete subgroups of G such that for any nonempty open set O of G, there exists an integer k such that , for every n ≥ k. It has been proved that the identity component of a Lie group approximable by discrete subgroups is nilpotent. In this paper we shall extend this result to pro-Lie groups. In particular, every connected locally compact group approximable by discrete subgroups is nilpotent. An application of discrete approximation is given.
- Subjects
LIE groups; FRATTINI subgroups; INTEGERS; NILPOTENT groups; COMPUTATIONAL mathematics
- Publication
Forum Mathematicum, 2016, Vol 28, Issue 1, p189
- ISSN
0933-7741
- Publication type
Article
- DOI
10.1515/forum-2014-0072