Minimal non-nilpotent groups which are supersolvable

TL;DR

This paper explores the structure of supersolvable groups that are minimal non-nilpotent, extending classic results to a broader class of groups and providing new insights into their subgroup properties.

Contribution

It generalizes existing descriptions of minimal non-nilpotent groups to the supersolvable case, broadening understanding of their subgroup structure.

Findings

Characterization of minimal non-nilpotent supersolvable groups

Extension of classic descriptions to supersolvable groups

Insights into subgroup nilpotency properties

Abstract

The structure of a group which is not nilpotent but all of whose proper subgroups are nilpotent has interested the researches of several authors both in the finite case and in the infinite case. The present paper generalizes some classic descriptions of M. Newman, H. Smith and J. Wiegold in the context of supersolvable groups.