Original scientific paper

https://doi.org/10.3336/gm.43.1.07

Minimal nonabelian and maximal subgroups of a finite p-group

Yakov Berkovich ; Department of Mathematics, University of Haifa

Abstract

The p-groups all of whose nonabelian maximal subgroups are either absolutely regular or of maximal class, are classified. For the main result of the papers by Cepulic and Pylavska, and Zhang, An and Xu, classifying the p-groups all of whose proper nonabelian subgroups are metacyclic, we offer a proof which is shorter and not so involved. In conclusion we study, in some detail, the p-groups containing an abelian maximal subgroup.

Keywords

Metacyclic p-groups; p-groups of maximal class; minimal nonabelian p-groups; absolutely regular p-groups; abelian maximal subgroups; maximal abelian normal subgroups

Hrčak ID:

23534

URI

https://hrcak.srce.hr/23534

Publication date:

25.5.2008.

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