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We define a class of discrete abelian group extensions of rank-onetransformations and establish necessary and sufficient conditions for theseextensions to be power weakly mixing. We show that all members of this classare multiply recurrent. We then study conditions sufficient for showing thatcartesian products of transformations are conservative for a class ofinvertible infinite measure-preserving transformations and provide examples ofthese transformations.

Ergodic properties of a class of discrete Abelian group extensions of rank-one transformations