Z-groups with continuous endomorphisms of finite topological entropy have closed derived subgroups whose continuous endomorphisms also have finite topological entropy.
Folland,A Course in Abstract Harmonic Analysis, CRC Press, 2016, Boca Raton
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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.