Powerfully solvable and powerfully simple groups

Iker de las Heras, Gunnar Traustason

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Abstract

We introduce the notion of a powerfully solvable group. These are powerful groups possessing an abelian series of a special kind. These groups include in particular the class of powerfully nilpotent groups. We will also see that for a certain rich class of powerful groups we can naturally introduce the term powerfully simple group and prove a Jordan-Hölder type theorem that justifies the term.

Original languageEnglish
Article number106714
JournalJournal of Pure and Applied Algebra
Volume225
Issue number8
Early online date19 Feb 2021
DOIs
Publication statusPublished - 31 Aug 2021

Bibliographical note

Funding Information:
The first author is supported by the Spanish Government grant MTM2017-86802-P , partly with FEDER funds, and by the Basque Government grant IT974-16 . He is also supported by a predoctoral grant of the University of the Basque Country .

Publisher Copyright:
© 2021 Elsevier B.V.

Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.

ASJC Scopus subject areas

  • Algebra and Number Theory

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