Algebraic entropy on topologically quasihamiltonian groups

W. Xi; M. Shlossberg; D. Toller

doi:10.1016/j.topol.2020.107093

Algebraic entropy on topologically quasihamiltonian groups

W. Xi, M. Shlossberg, D. Toller

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

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Abstract

We study the algebraic entropy of continuous endomorphisms of compactly covered, locally compact, topologically quasihamiltonian groups. We provide a Limit-free formula which helps us to simplify the computations of this entropy. Moreover, several Addition Theorems are given. In particular, we prove that the Addition Theorem holds for every group endomorphism of a quasihamiltonian torsion FC-group (e.g., a Hamiltonian group).

Original language	English
Article number	107093
Journal	Topology and its Applications
Volume	272
DOIs	https://doi.org/10.1016/j.topol.2020.107093
State	Published - 1 Mar 2020
Externally published	Yes

Bibliographical note

Publisher Copyright:
© 2020

Funding

It is a pleasure to thank the referee for the careful reading and the invaluable suggestions that led us to extend Lemma 3.4 , Lemma 5.2 , and Corollary 5.3 to their actual form. We thank Wolfgang Herfort for sharing with us some of the secrets of the tqh groups. Thanks are due also to Anna Giordano Bruno and Dikran Dikranjan for several suggestions on the first draft of this paper. The first-named author takes this opportunity to thank Dikran Dikranjan for his generous hospitality and support. The second and third-named authors have been supported by Programma SIR 2014 by MIUR , project GADYGR, number RBSI14V2LI , cup G22I15000160008. The third-named author has been supported by grant PDM_VQR3_DMIF_ASSEGNI_DI_RICERCA of Udine University . It is a pleasure to thank the referee for the careful reading and the invaluable suggestions that led us to extend Lemma 3.4, Lemma 5.2, and Corollary 5.3 to their actual form. We thank Wolfgang Herfort for sharing with us some of the secrets of the tqh groups. Thanks are due also to Anna Giordano Bruno and Dikran Dikranjan for several suggestions on the first draft of this paper. The first-named author takes this opportunity to thank Dikran Dikranjan for his generous hospitality and support. The second and third-named authors have been supported by Programma SIR 2014 by MIUR, project GADYGR, number RBSI14V2LI, cup G22I15000160008. The third-named author has been supported by grant PDM_VQR3_DMIF_ASSEGNI_DI_RICERCA of Udine University.

Funders	Funder number
Udine University
Ministero dellâIstruzione, dellâUniversitÃ e della Ricerca	G22I15000160008
Università degli Studi di Udine

Keywords

(Topologically) quasihamiltonian group
Addition Theorem
Algebraic entropy
Compactly covered group
Hamiltonian group

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10.1016/j.topol.2020.107093

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abstract = "We study the algebraic entropy of continuous endomorphisms of compactly covered, locally compact, topologically quasihamiltonian groups. We provide a Limit-free formula which helps us to simplify the computations of this entropy. Moreover, several Addition Theorems are given. In particular, we prove that the Addition Theorem holds for every group endomorphism of a quasihamiltonian torsion FC-group (e.g., a Hamiltonian group).",

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Algebraic entropy on topologically quasihamiltonian groups

Abstract

Bibliographical note

Funding

Keywords

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