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Algebraic entropy on topologically quasihamiltonian groups. (English) Zbl 1439.54011
Summary: We study the algebraic entropy of continuous endomorphisms of compactly covered, locally compact, topologically quasihamiltonian groups. We provide a Limit-free formula which helps us to simplify the computations of this entropy. Moreover, several Addition Theorems are given. In particular, we prove that the Addition Theorem holds for every group endomorphism of a quasihamiltonian torsion FC-group (e.g., a Hamiltonian group).

MSC:
54C70 Entropy in general topology
54H11 Topological groups (topological aspects)
37A35 Entropy and other invariants, isomorphism, classification in ergodic theory
22D40 Ergodic theory on groups
28D20 Entropy and other invariants
20K35 Extensions of abelian groups
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