Orbits of Distal Actions on Locally Compact Groups

Riddhi Shah

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arXiv · 1010.5735

Orbits of Distal Actions on Locally Compact Groups

Riddhi Shah

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Abstract

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 has [MOC].

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BibTeX RIS

Riddhi Shah. 2010-10-27. Orbits of Distal Actions on Locally Compact Groups. https://arxiv.org/abs/1010.5735

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