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Frontiers of Mathematics in China

, Volume 13, Issue 4, pp 763–777 | Cite as

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

  • Lijian An
Research Article

Abstract

Suppose that G is a finite p-group. If G is not a Dedekind group, then G has a non-normal subgroup. We use pM(G) and pm(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) < 2m(G)‒1: As a by-product, we also classify p-groups whose orders of non-normal subgroups are pk and pk+1.

Keywords

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

MSC

20D15 

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Notes

Acknowledgements

This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 11471198, 11771258).

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Copyright information

© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsShanxi Normal UniversityLinfenChina

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