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, Bibcode:1942PNAS...28..254H, doi:10.1073/pnas.28.6.254, ISSN 0027-8424, JSTOR 87587, MR 0006543, PMC 1078459, PMID 16578045
• van Dantzig, D. (1933), "Zur topologischen Algebra", Mathematische Annalen, 107, Springer Berlin / Heidelberg: 587–626, doi:10.1007/BF01448911, ISSN 0025-5831, S2CID 115662380