Some finite p-groups whose normal subgroups are characteristic

Abstract

In this article, we classify some finite p-groups whose normal subgroups are characteristic. Particularly we restrict our attention to all finite p-groups of maximal class with an abelian maximal subgroup, finite 3-groups of maximal class, finite split metacyclic p-groups, minimal non-abelian p-groups and all p-groups of maximal class of order less than p⁶.

Keywords:

• p-Groups of maximal class
• characteristic subgroup

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 20D45
• 20D15

Acknowledgment

The authors are grateful to the referee for his valuable suggestions. The article was revised according to his comments.