Generators of Monothetic Groups
Canadian journal of mathematics, Tome 23 (1971) no. 5, pp. 791-796
Voir la notice de l'article provenant de la source Cambridge University Press
A topological group G is called monothetic if it contains a dense cyclic subgroup. An element x of G is called a generator of G if x generates a dense cyclic subgroup of G. We denote by E(G) the set of generators of G; the complement of E(G) in G, consisting of the “non-generators” of G, we write as N(G) Throughout this paper we consider only locally compact abelian (LCA) groups satisfying the T2 separation axiom (note that a monothetic group is automatically abelian). In [1] certain problems of measurability concerning the set E(G) are discussed. In this paper we shall consider some algebraic and topological properties of the sets E(G) and N(G)
Armacost, D. L. Generators of Monothetic Groups. Canadian journal of mathematics, Tome 23 (1971) no. 5, pp. 791-796. doi: 10.4153/CJM-1971-087-7
@article{10_4153_CJM_1971_087_7,
author = {Armacost, D. L.},
title = {Generators of {Monothetic} {Groups}},
journal = {Canadian journal of mathematics},
pages = {791--796},
year = {1971},
volume = {23},
number = {5},
doi = {10.4153/CJM-1971-087-7},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1971-087-7/}
}
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[3] 3. Kaplansky, I., Infinite abelian groups (University of Michigan Press, Ann Arbor, 1954). Google Scholar
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