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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Gianazza, Ugo / Vespri, Vincenzo


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2391-5455
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Volume 11, Issue 12

Issues

Volume 13 (2015)

Groups with every subgroup ascendant-by-finite

Sergio Camp-Mora
  • Departamento de Matemática Aplicada, Universidad Politécnica de Valencia, Camino de Vera s/n, 46022, Valencia, Spain
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Published Online: 2013-10-08 | DOI: https://doi.org/10.2478/s11533-013-0312-y

Abstract

A subgroup H of a group G is called ascendant-by-finite in G if there exists a subgroup K of H such that K is ascendant in G and the index of K in H is finite. It is proved that a locally finite group with every subgroup ascendant-by-finite is locally nilpotent-by-finite. As a consequence, it is shown that the Gruenberg radical has finite index in the whole group.

MSC: 20F19; 20F22; 20F50

Keywords: Ascendant subgroup; Locally nilpotent; Radical; Locally finite group

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About the article

Published Online: 2013-10-08

Published in Print: 2013-12-01


Citation Information: Open Mathematics, Volume 11, Issue 12, Pages 2182–2185, ISSN (Online) 2391-5455, DOI: https://doi.org/10.2478/s11533-013-0312-y.

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© 2013 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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