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Acta Mathematica Sinica, English Series

, Volume 35, Issue 7, pp 1179–1189 | Cite as

Finite p-groups All of Whose Minimal Nonabelian Subgroups are Nonmetacyclic of Order p3

  • Qin Hai ZhangEmail author
Article
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Abstract

Assume p is an odd prime. We investigate finite p-groups all of whose minimal nonabelian subgroups are of order p3. Let \(\mathcal{P}_1\)-groups denote the p-groups all of whose minimal nonabelian subgroups are nonmetacyclic of order p3. In this paper, the \(\mathcal{P}_1\)-groups are classified, and as a by-product, we prove the Hughes’ conjecture is true for the \(\mathcal{P}_1\)-groups.

Keywords

Finite p-groups a minimal nonabelian subgroup the Hughes subgroup p-groups of maximal class 

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Copyright information

© Springer-Verlag GmbH Germany & The Editorial Office of AMS 2019

Authors and Affiliations

  1. 1.Department of MathematicsShanxi Normal UniversityLinfenP. R. China

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