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In this note, we study the normal compact K\"ahler (possibly singular)threefold $X$ admitting the action of a free abelian group $G$ of maximal rank,all the non-trivial elements of which are of positive entropy. If such $X$ isfurther assumed to have only terminal singularities, then we prove that it iseither a rationally connected projective threefold or bimeromorphic to aquasi-\'etale quotient of a complex $3$-torus.

Compact K\"ahler threefolds with the action of an abelian group of maximal rank