2020/06/22 by Heras, Iker de las, Traustason, Gunnar
#FOS: Mathematics #Group Theory (math.GR)
paper · doi:10.48550/arxiv.2006.12593
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.