The intrinsic algebraic entropy ent(ɸ) of an endomorphism ɸ of an Abelian group G can be computed using fully inert subgroups of ɸ-invariant sections of G, instead of the whole family of ɸ-inert subgroups. For a class of groups containing the groups of finite rank, aswell as those groupswhich are trajectories of finitely generated subgroups, it is proved that only fully inert subgroups of the group itself are needed to comput ent(ɸ). Examples show how the situation may be quite different outside of this class.
@article{bwmeta1.element.doi-10_1515_taa-2015-0005,
author = {Brendan Goldsmith and Luigi Salce},
title = {When the intrinsic algebraic entropy is not really intrinsic},
journal = {Topological Algebra and its Applications},
volume = {3},
year = {2015},
zbl = {1326.37006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_taa-2015-0005}
}
Brendan Goldsmith; Luigi Salce. When the intrinsic algebraic entropy is not really intrinsic. Topological Algebra and its Applications, Tome 3 (2015) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_taa-2015-0005/
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