Algebraic entropy on strongly compactly covered groups

Anna Giordano Bruno; Menachem Shlossberg; Daniele Toller

doi:10.1016/j.topol.2019.05.022

Algebraic entropy on strongly compactly covered groups

Anna Giordano Bruno, Menachem Shlossberg, Daniele Toller

Research output: Contribution to journal › Article › peer-review

11 Scopus citations

Abstract

We introduce a new class of locally compact groups, namely the strongly compactly covered groups, which are the Hausdorff topological groups G such that every element of G is contained in a compact open normal subgroup of G. For continuous endomorphisms ϕ:G→G of these groups we compute the algebraic entropy and study its properties. Also an Addition Theorem is available under suitable conditions.

Original language	English
Pages (from-to)	117-140
Number of pages	24
Journal	Topology and its Applications
Volume	263
DOIs	https://doi.org/10.1016/j.topol.2019.05.022
State	Published - 15 Aug 2019
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2019 The Authors

Funding

This work is supported by Programma SIR 2014 by MIUR, project GADYGR, number RBSI14V2LI , cup G22I15000160008 .

Funders	Funder number
Ministero dell’Istruzione, dell’Università e della Ricerca	G22I15000160008

Keywords

Addition Theorem
Algebraic entropy
Bridge Theorem
Compactly covered group
Continuous endomorphism
Discrete dynamical system
FC-group
Limit-free Formula
Locally compact group
Locally finite group
Strongly compactly covered group

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10.1016/j.topol.2019.05.022

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AU - Shlossberg, Menachem

AU - Toller, Daniele

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AB - We introduce a new class of locally compact groups, namely the strongly compactly covered groups, which are the Hausdorff topological groups G such that every element of G is contained in a compact open normal subgroup of G. For continuous endomorphisms ϕ:G→G of these groups we compute the algebraic entropy and study its properties. Also an Addition Theorem is available under suitable conditions.

KW - Addition Theorem

KW - Algebraic entropy

KW - Bridge Theorem

KW - Compactly covered group

KW - Continuous endomorphism

KW - Discrete dynamical system

KW - FC-group

KW - Limit-free Formula

KW - Locally compact group

KW - Locally finite group

KW - Strongly compactly covered group

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SN - 0166-8641

VL - 263

SP - 117

EP - 140

JO - Topology and its Applications

JF - Topology and its Applications

ER -

Algebraic entropy on strongly compactly covered groups

Abstract

Bibliographical note

Funding

Keywords

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