Glasnik Matematicki, Vol. 43, No.1 (2008), 97-109.

MINIMAL NONABELIAN AND MAXIMAL SUBGROUPS OF A FINITE p-GROUP

Yakov Berkovich

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.

2000 Mathematics Subject Classification.   20D15.

Key words and phrases.   Metacyclic p-groups, p-groups of maximal class, minimal nonabelian p-groups, absolutely regular p-groups, abelian maximal subgroups, maximal abelian normal subgroups.

DOI: 10.3336/gm.43.1.07

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