We classify finite p-groups all of whose nonnormal subgroups have orders at most p3, p odd prime. Together with a known result, we completely solved Problem 2279 proposed by Y. Berkovich and Z. Janko in Groups of Prim...We classify finite p-groups all of whose nonnormal subgroups have orders at most p3, p odd 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.展开更多
基金Acknowledgements The authors cordially thank the referees for detailed and valuable comments, which help them to improve the paper. This work was supported by the National Natural Science Foundation of China （Grant Nos. 11371232, 11101252）, the Natural Science Foundation of Shanxi Province （No. 2012011001, 2013011001）, and Shanxi Scholarship Council of China （No. [201118）.
文摘We classify finite p-groups all of whose nonnormal subgroups have orders at most p3, p odd 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.
