Finite <i>p</i>-groups whose non-normal subgroups have few orders

doi:10.1007/s11464-018-0693-0

Front. Math. China

2018, Vol. 13

Issue (4) : 763-777 https://doi.org/10.1007/s11464-018-0693-0

RESEARCH ARTICLE

Finite p-groups whose non-normal subgroups have few orders

Lijian AN(

)

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

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Abstract

Suppose that G is a nite p-group. If G is not a Dedekind group, then G has a non-normal subgroup. We use $p M (G)$ and $p m (G)$ to denote the maximum and minimum of the orders of the non-normal subgroups of G; respectively. In this paper, we classify groups G such that $M (G) 〈 2 m (G) − 1$ : As a by-product, we also classify p-groups whose orders of non-normal subgroups are $p k$ and $p k + 1$ :

Keywords Finite p-groups meta-hamiltonian p-groups non-normal subgroups

Corresponding Author(s): Lijian AN

Issue Date: 14 August 2018

Cite this article:

Lijian AN. Finite p-groups whose non-normal subgroups have few orders[J]. Front. Math. China, 2018, 13(4): 763-777.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-018-0693-0
https://academic.hep.com.cn/fmc/EN/Y2018/V13/I4/763

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[1]	Qiangwei SONG, Qinhai ZHANG. Finite 2-groups whose length of chain of nonnormal subgroups is at most 2[J]. Front. Math. China, 2018, 13(5): 1075-1097.

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