Abelian groups of zero adjoint entropy

L. Salce, and P. Zanardo. "Abelian groups of zero adjoint entropy." Colloquium Mathematicae 121.1 (2010): 45-62. <http://eudml.org/doc/284201>.

@article{L2010,
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.},
author = {L. Salce, P. Zanardo},
journal = {Colloquium Mathematicae},
keywords = {adjoint entropy; algebraic entropy; endomorphisms of Abelian groups; mixed Abelian groups},
language = {eng},
number = {1},
pages = {45-62},
title = {Abelian groups of zero adjoint entropy},
url = {http://eudml.org/doc/284201},
volume = {121},
year = {2010},
}

TY - JOUR
AU - L. Salce
AU - P. Zanardo
TI - Abelian groups of zero adjoint entropy
JO - Colloquium Mathematicae
PY - 2010
VL - 121
IS - 1
SP - 45
EP - 62
AB - 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.
LA - eng
KW - adjoint entropy; algebraic entropy; endomorphisms of Abelian groups; mixed Abelian groups
UR - http://eudml.org/doc/284201
ER -