Finite 2-groups whose nonnormal subgroups have orders at most 2<sup>3

doi:10.1007/s11464-012-0216-3

Front Math Chin

2012, Vol. 7

Issue (5) : 971-1003 https://doi.org/10.1007/s11464-012-0216-3

RESEARCH ARTICLE

Finite 2-groups whose nonnormal subgroups have orders at most 2³

Qinhai ZHANG(

), Meijuan SU

Department of Mathematics, Shanxi Normal University, Linfen 041004, China

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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.

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

Corresponding Author(s): ZHANG Qinhai,Email:zhangqh@sxnu.edu.cn

Issue Date: 01 October 2012

Cite this article:

Qinhai ZHANG,Meijuan SU. Finite 2-groups whose nonnormal subgroups have orders at most 2^{3[J]. Front Math Chin,
2012, 7(5): 971-1003.}

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-012-0216-3
https://academic.hep.com.cn/fmc/EN/Y2012/V7/I5/971

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[3]	Qinhai ZHANG,Xiaoxiao LI,Meijuan SU. Finite p-groups whose nonnormal subgroups have orders at most p³[J]. Front. Math. China, 2014, 9(5): 1169-1194.
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[6]	Dong LIU, Linsheng ZHU. Generalized Heisenberg-Virasoro algebras[J]. Front Math Chin, 2009, 4(2): 297-310.

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