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 language | English |
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Article number | 106714 |
Journal | Journal of Pure and Applied Algebra |
Volume | 225 |
Issue number | 8 |
Early online date | 19 Feb 2021 |
DOIs | |
Publication status | Published - 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.
Funding
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 .
ASJC Scopus subject areas
- Algebra and Number Theory