Finite p-groups whose non-normal subgroups have few orders
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 p k and pk+1.
KeywordsFinite p-groups meta-hamiltonian p-groups non-normal subgroups
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This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 11471198, 11771258).
- 4.Fang X, An L. The classification of finite metahamiltonian p-groups. arXiv.org: 1310.5509v2Google Scholar