For an arbitrary set A ⊆ ℕ satisfying 1 ∈ A and lcm(m₁,m₂) ∈ A whenever m₁,m₂ ∈ A, an ergodic abelian group extension of a rotation for which the range of the multiplicity function equals A is constructed.
@article{bwmeta1.element.bwnjournal-article-smv102i2p157bwm,
author = {G. Goodson and J. Kwiatkowski and M. Lema\'nczyk and P. Liardet},
title = {On the multiplicity function of ergodic group extensions of rotations},
journal = {Studia Mathematica},
volume = {103},
year = {1992},
pages = {157-174},
zbl = {0830.28009},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv102i2p157bwm}
}
Goodson, G.; Kwiatkowski, J.; Lemańczyk, M.; Liardet, P. On the multiplicity function of ergodic group extensions of rotations. Studia Mathematica, Tome 103 (1992) pp. 157-174. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv102i2p157bwm/
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