Powerfully solvable and powerfully simple groups

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-Holder type theorem that justifies the term. (C) 2021 Elsevier B.V. All rights reserved.