Additivity of the algebraic entropy for locally finite groups with permutable finite subgroups

The additivity with respect to exact sequences is notoriously a fundamental property of the algebraic entropy of group endomorphisms. It was proved for abelian groups by deeply exploiting their structure. On the other hand, a solvable counterexample was recently found, showing that it does not hold in general. Nevertheless, we give a rather short proof of the additivity of the algebraic entropy for locally finite groups that are either quasihamiltonian or FC-groups.

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