Groups with the real chain condition on non-pronormal subgroups

TL;DR

This paper characterizes generalized radical groups that lack certain infinite chains of non-pronormal subgroups, showing they are either minimax or have all subgroups pronormal, thus linking subgroup chain properties to group structure.

Contribution

It provides a complete characterization of generalized radical groups with no real chain of non-pronormal subgroups, connecting subgroup chain conditions to group classification.

Findings

Groups with no real chain of non-pronormal subgroups are either minimax or have all subgroups pronormal.

The result links subgroup chain properties to the overall structure of the group.

Provides a criterion for the absence of certain infinite subgroup chains in generalized radical groups.

Abstract

It is shown that a gerenalised radical group has no chain of non-pronormal subgroups with the same order type as the set of the real numbers if and only if either the group is minimax or all subgroups are pronormal.