Submission date: 4 July 2010.

Abstract:

We study relationships between certain algebraic properties of groups and rings definable in a first order structure or *-closed in a compact G-space. As a consequence, we obtain a few structural results about \omega-categorical rings as well as about small, nm-stable compact G-rings, and we also obtain surprising relationships between some conjectures concerning small profinite groups.

Mathematics Subject Classification: 03C45, 03C35, 20A15

Keywords and phrases: \omega-categorical group, \omega-categorical ring, small compact G-group, small compact G-ring

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