When the intrinsic algebraic entropy is not really intrinsic

Brendan Goldsmith; Luigi Salce

Topological Algebra and its Applications (2015)

  • Volume: 3, Issue: 1, page 45-56, electronic only
  • ISSN: 2299-3231

Abstract

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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.

How to cite

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Brendan Goldsmith, and Luigi Salce. "When the intrinsic algebraic entropy is not really intrinsic." Topological Algebra and its Applications 3.1 (2015): 45-56, electronic only. <http://eudml.org/doc/275888>.

@article{BrendanGoldsmith2015,
abstract = {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.},
author = {Brendan Goldsmith, Luigi Salce},
journal = {Topological Algebra and its Applications},
keywords = {Abelian groups; intrinsic algebraic entropy; fully inert subgroups; abelian groups},
language = {eng},
number = {1},
pages = {45-56, electronic only},
title = {When the intrinsic algebraic entropy is not really intrinsic},
url = {http://eudml.org/doc/275888},
volume = {3},
year = {2015},
}

TY - JOUR
AU - Brendan Goldsmith
AU - Luigi Salce
TI - When the intrinsic algebraic entropy is not really intrinsic
JO - Topological Algebra and its Applications
PY - 2015
VL - 3
IS - 1
SP - 45
EP - 56, electronic only
AB - 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.
LA - eng
KW - Abelian groups; intrinsic algebraic entropy; fully inert subgroups; abelian groups
UR - http://eudml.org/doc/275888
ER -

References

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