Journal of Lie Theory 22 (2012), No. 2, 587--599
Copyright Heldermann Verlag 2012
Orbits of Distal Actions on Locally Compact Groups
School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
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].
Keywords: Distal group actions, Minimal orbit closures, Generalised FC-groups.
MSC: 37B05; 22D05, 22D45
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