Abstract
The groups as mentioned in the title are classified up to isomorphism. This is an answer to a question proposed by Berkovich and Janko.
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Berkovich, Y., Groups of Prime Power Order, Vol. 1, Walter de Gruyter, Berlin, New York, 2008.
Berkovich, Y. and Janko, Z., Groups of Prime Power Order, Vol. 2, Walter de Gruyter, Berlin, New York, 2008.
Berkovich, Y. and Janko, Z., Groups of Prime Power Order, Vol. 3, Walter de Gruyter, Berlin, New York, 2011.
Rédei, L., Das schiefe produkt in der Gruppentheorie, Comment. Math. Helvet, 20, 1947, 225–267.
Zhang, J. Q. and Li, X. H., Finite p-groups all of whose proper subgroups have small derived subgoups, Sci. China Ser. A, 53, 2010, 1357–1362.
Blackburn, N., Generalizations of certain elementary theorems on p-groups, Proc. London Math. Soc., 11(3), 1961, 1–22.
Newman, M. F. and Xu, M. Y., Metacyclic groups of prime power oder, Chin. Adv. Math., 17, 1988, 106–107.
Xu, M. Y. and Zhang, Q. H., A classification of metacyclic 2-groups, Algebra Colloq., 13(1), 2006, 25–34.
Xu, M. Y. and Qu, H. P., Finite p-Groups (in Chinese), Beijing University Press, Beijing, 2010.
Xu, M. Y., An, L. J. and Zhang, Q. H., Finite p-groups all of whose non-abelian proper subgroups are generated by two elements, J. Algebra, 319, 2008, 3603–3620.
Xu, M. Y., An Introduction to Finite Groups I (in Chinese), 2nd edition, Scientific Press, Beijing, 1999.
Zhang, Q. H., Song, Q. W. and Xu, M. Y., The classification of some regular p-groups and its applications, Sci. China Ser. A, 49(3), 2006, 366–386.
An, L. J., Li, L. L., Qu, H. P. and Zhang, Q. H., Finite p-groups with a minimal non-abelian subgroup of index p (II), Sci. China Ser. A, 57(4), 2014, 737–753.
Li, L. L., Qu, H. P. and Chen, G. Y., Central extension of inner abelian p-groups (I), Acta Math. Sinica, Chinese Series, 53(4), 2010, 675–684.
Janko, Z., Finite 2-groups with exactly one nonmetacyclic maximal subgroup, Israel J. Math., 166, 2008, 313–347.
An, L. J., Hu, R. F. and Zhang, Q. H., Finite p-groups with a minimal non-abelian subgroup of index p (IV), J. Algebra Appl., to appear.
Qu, H. P., Xu, M. Y. and An, L. J., Finite p-groups with a minimal non-abelian subgroup of index p (III), Sci. China Ser. A, to appear.
Berkovich, Y., On subgroups of finite p-groups, J. Algebra, 224, 2000, 198–240.
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This work was supported by the National Natural Science Foundation of China (Nos. 11371232, 11101252), the Shanxi Provincial Natural Science Foundation of China (No. 2013011001) and the Fundamental Research Funds for the Central Universities (No.BUPT2013RC0901).
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Zhang, L., Xia, Y. & Zhang, Q. Finite p-groups all of whose maximal subgroups either are metacyclic or have a derived subgroup of order ≤ p . Chin. Ann. Math. Ser. B 36, 11–30 (2015). https://doi.org/10.1007/s11401-014-0880-6
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DOI: https://doi.org/10.1007/s11401-014-0880-6