Journal of Lie Theory 22 (2012), No. 2, 587--599
Copyright Heldermann Verlag 2012
Orbits of Distal Actions on Locally Compact Groups
Riddhi Shah
School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
rshah@mail.jnu.ac.in
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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