On minimal non-PE-groups (Q1295621)

A subgroup \(H\) of the finite group \(G\) is an NE-subgroup of \(G\) if it is the intersection of its normalizer and its normal closure; \(G\) is PE-group if all of its minimal subgroups are NE-subgroups of \(G\). The author shows that a PE-group (1) contains a PN-group (a group in which every minimal subgroup is normal) and (2) is solvable with Fitting height at most 3. Then he classifies the minimal non-PE-groups (i.e., non-PE-groups whose proper subgroups are all PE-groups).