Powerfully solvable and powerfully simple groups

Iker de las Heras; Gunnar Traustason

doi:10.1016/j.jpaa.2021.106714

Powerfully solvable and powerfully simple groups

Iker de las Heras, Gunnar Traustason

Department of Mathematical Sciences

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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 language	English
Article number	106714
Journal	Journal of Pure and Applied Algebra
Volume	225
Issue number	8
Early online date	19 Feb 2021
DOIs	https://doi.org/10.1016/j.jpaa.2021.106714
Publication status	Published - 31 Aug 2021

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jpaa.2021.106714

PSolvSimpleNEW.PDFAccepted author manuscript, 294 KBLicence: CC BY-NC-ND

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N2 - 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.

AB - 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.

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Powerfully solvable and powerfully simple groups

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