Abelian groups of zero adjoint entropy
Tom 121 / 2010
Colloquium Mathematicum 121 (2010), 45-62
MSC: 20K30, 28D20.
DOI: 10.4064/cm121-1-5
Streszczenie
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.
