Powerfully solvable and powerfully simple groups

Iker de las Heras; Gunnar Traustason

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arXiv · 2006.12593

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-H\"older type theorem that justifies the term.

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Iker de las Heras, Gunnar Traustason. 2020-06-22. Powerfully solvable and powerfully simple groups. https://arxiv.org/abs/2006.12593

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