Monothetic group

In mathematics, a monothetic group is a topological group with a dense cyclic subgroup. They were introduced by Van Dantzig (1933). An example is the additive group of p-adic integers, in which the integers are dense. A monothetic group is necessarily abelian.

References

• Kuipers, L.; Niederreiter, H. (2006) [1974], Uniform Distribution of Sequences, Dover Publishing, ISBN 0-486-45019-8 
• Halmos, Paul R.; Samelson, Hans (1942), "On monothetic groups", Proceedings of the National Academy of Sciences of the United States of America 28 (6): 254–258, doi:10.1073/pnas.28.6.254, ISSN 0027-8424, PMID 16578045, Bibcode: 1942PNAS...28..254H 
• van Dantzig, D. (1933), "Zur topologischen Algebra", Mathematische Annalen (Springer Berlin / Heidelberg) 107: 587–626, doi:10.1007/BF01448911, ISSN 0025-5831