Journal of Lie Theory

no. 2
Orbits of Distal Actions on Locally Compact Groups
Journal of Lie Theory, Volume 22 (2012) no. 2, pp. 587-599
We discuss properties of orbits of (semi)group actions on locally compact groups G. In particular, we show that if a compactly generated locally compact abelian group acts distally on G then the closure of each of its orbits is a minimal closed invariant set (i.e. the action has [MOC]). We also show that for such an action distality is preserved if we go modulo any closed normal invariant subgroup and hence [MOC] is also preserved. We also show that any semigroup action on G has [MOC] if and only if the corresponding actions on a compact invariant metrizable subgroup K and on the quotient space G/K have [MOC].
DOI: 10.5802/jolt.683
Classification: 37B05, 22D05, 22D45
Keywords: Distal group actions, Minimal orbit closures, Generalised FC-groups 
@article{JOLT_2012_22_2_a12,
     author = {R. Shah},
     title = {Orbits of {Distal} {Actions} on {Locally} {Compact} {Groups}},
     journal = {Journal of Lie Theory},
     pages = {587--599},
     year = {2012},
     volume = {22},
     number = {2},
     doi = {10.5802/jolt.683},
     zbl = {1254.37011},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.683/}
}
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R. Shah. Orbits of Distal Actions on Locally Compact Groups. Journal of Lie Theory, Volume 22 (2012) no. 2, pp. 587-599. doi: 10.5802/jolt.683

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