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.

Key words： Minimal non-abelian p-group; nonnormal subgroup; central extension

References

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