Abstract
In this paper, we classify finite 2-groups all of whose nonnormal subgroups have orders at most 23. 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.
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References
Berkovich Y. Groups of Prime Power Order, Vol. 1. Berlin, New York: Walter de Gruyter, 2008
Berkovich Y, Janko Z. Groups of Prime Power Order, Vol. 2. Berlin, New York: Walter de Gruyter, 2008
Berkovich Y, Janko Z. Groups of Prime Power Order, Vol. 3. Berlin, New York: Walter de Gruyter, 2011
Huppert B. Endliche Gruppen I. Berlin, Heidelberg, New York: Springer-Verlag, 1967
Passman D S. Nonnormal subgroups of p-groups. J Algebra, 1970, 15: 352–370
Zhang G H, Guo X Q, Qu H P, Xu M Y. Finite group which have many normal subgroups. J Korean Math Soc, 2009, 46(6): 1165–1178
Zhang Q H, Li X X, Su M J. Finite p-groups whose nonnormal subgroups have orders ⩾ p 3 (in preparation)
Zhang Q H, Sun X J, An L J, Xu M Y. Finite p-groups all of whose subgroups of index p 2 are abelian. Algebra Colloq, 2008, 15(1): 167–180
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Zhang, Q., Su, M. Finite 2-groups whose nonnormal subgroups have orders at most 23 . Front. Math. China 7, 971–1003 (2012). https://doi.org/10.1007/s11464-012-0216-3
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DOI: https://doi.org/10.1007/s11464-012-0216-3