RESEARCH ARTICLE

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

  • Lijian AN
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  • Department of Mathematics, Shanxi Normal University, Linfen 041004, China

Received date: 21 Dec 2017

Accepted date: 26 Feb 2018

Published date: 14 Aug 2018

Copyright

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

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 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:

Cite this article

Lijian AN . Finite p-groups whose non-normal subgroups have few orders[J]. Frontiers of Mathematics in China, 2018 , 13(4) : 763 -777 . DOI: 10.1007/s11464-018-0693-0

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