Z-groups with continuous endomorphisms of finite topological entropy have closed derived subgroups whose continuous endomorphisms also have finite topological entropy.
Takahashi, A duality theorem for representable locally compact groups with compact commutator subgroup, Tohoku Math
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A dynamical approach to Schur's Theorem
Z-groups with continuous endomorphisms of finite topological entropy have closed derived subgroups whose continuous endomorphisms also have finite topological entropy.