Abelian groups of zero adjoint entropy

Volume 121 / 2010

L. Salce, P. Zanardo Colloquium Mathematicum 121 (2010), 45-62 MSC: 20K30, 28D20. DOI: 10.4064/cm121-1-5

Abstract

The notion of adjoint entropy for endomorphisms of an Abelian group is somehow dual to that of algebraic entropy. The Abelian groups of zero adjoint entropy, i.e. ones whose endomorphisms all have zero adjoint entropy, are investigated. Torsion groups and cotorsion groups satisfying this condition are characterized. It is shown that many classes of torsionfree groups contain groups of either zero or infinite adjoint entropy. In particular, no characterization of torsionfree groups of zero adjoint entropy is possible. It is also proved that the mixed groups of a wide class all have infinite adjoint entropy.

Authors

  • L. SalceDipartimento di Matematica Pura e Applicata
    Università di Padova
    Via Trieste 63
    35121 Padova, Italy
    e-mail
  • P. ZanardoDipartimento di Matematica Pura e Applicata
    Università di Padova
    Via Trieste 63
    35121 Padova, Italy
    e-mail

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