Finite p-groups whose nonnormal subgroups are metacyclic

For an odd prime p , we give a criterion for finite p -groups whose nonnormal subgroups are metacyclic, and based on the criterion, the p -groups whose nonnormal subgroups are metacyclic are classifid up to isomorphism. This solves a problem proposed by Berkovich.

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Veröffentlicht in:	Science China. Mathematics 2020-07, Vol.63 (7), p.1271-1284
Hauptverfasser:	Song, Qiangwei, Qu, Haipeng
Format:	Artikel
Sprache:	eng
Schlagworte:	Applications of Mathematics Criteria Isomorphism Mathematics Mathematics and Statistics Subgroups
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Beschreibung
Zusammenfassung:	For an odd prime p , we give a criterion for finite p -groups whose nonnormal subgroups are metacyclic, and based on the criterion, the p -groups whose nonnormal subgroups are metacyclic are classifid up to isomorphism. This solves a problem proposed by Berkovich.
ISSN:	1674-7283 1869-1862
DOI:	10.1007/s11425-018-9479-1