Let G be a Polish group and let H≤G be a compact subgroup. We prove that there exists a Borel set T⊂G which is simultaneously a complete set of coset representatives of left and right cosets, provided that a certain index condition is satisfied. Moreover, we prove that this index condition holds provided that G is locally compact and G/G∘ is compact or H is a compact Lie group. This generalizes a result which is known for discrete groups under various finiteness assumptions, but is known to fail for general inclusions of infinite groups. As an application, we prove that Bohr closed subgroups of countable, discrete groups admit common transversals.
Hiroshi Ando; Andreas Thom. Common transversals for coset spaces of compact groups. Groups, geometry, and dynamics, Tome 19 (2025) no. 2, pp. 397-414. doi: 10.4171/ggd/879
@article{10_4171_ggd_879,
author = {Hiroshi Ando and Andreas Thom},
title = {Common transversals for coset spaces of compact groups},
journal = {Groups, geometry, and dynamics},
pages = {397--414},
year = {2025},
volume = {19},
number = {2},
doi = {10.4171/ggd/879},
url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/879/}
}
TY - JOUR
AU - Hiroshi Ando
AU - Andreas Thom
TI - Common transversals for coset spaces of compact groups
JO - Groups, geometry, and dynamics
PY - 2025
SP - 397
EP - 414
VL - 19
IS - 2
UR - http://geodesic.mathdoc.fr/articles/10.4171/ggd/879/
DO - 10.4171/ggd/879
ID - 10_4171_ggd_879
ER -
%0 Journal Article
%A Hiroshi Ando
%A Andreas Thom
%T Common transversals for coset spaces of compact groups
%J Groups, geometry, and dynamics
%D 2025
%P 397-414
%V 19
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4171/ggd/879/
%R 10.4171/ggd/879
%F 10_4171_ggd_879
