Finite p-groups whose nonnormal subgroups have orders at most p³

Abstract

We classify finite p-groups all of whose nonnormal subgroups have orders at most p³, podd prime. Together with a known result, we completely solved Problem 2279 proposed by Y. Berkovich and Z. Janko in Groups of Prime Power Order, Vol. 3.

Keywords

Minimal non-abelian p-group / nonnormal subgroup / central extension

References

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RIGHTS & PERMISSIONS

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg