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.
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Acknowledgements
This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 11471198, 11771258).
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An, L. Finite p-groups whose non-normal subgroups have few orders. Front. Math. China 13, 763–777 (2018). https://doi.org/10.1007/s11464-018-0693-0
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DOI: https://doi.org/10.1007/s11464-018-0693-0