Finite p-groups in which the normal closure of each non-normal cyclic subgroup is nonabelian

• Verfasst von: Janko, Zvonimir [VerfasserIn]
• Titel: Finite p-groups in which the normal closure of each non-normal cyclic subgroup is nonabelian
• Verf.angabe: Zvonimir Janko
• E-Jahr: 2014
• Jahr: December 2014
• Umfang: 4 S.
• Fussnoten: Gesehen am 22.02.2018
• Titel Quelle: Enthalten in: Glasnik matematički
• Ort Quelle: Zagreb : Društvo, 1966
• Jahr Quelle: 2014
• Band/Heft Quelle: 49(2014), 2, Seite 333-336
• ISSN Quelle: 1846-7989
• DOI: doi:10.3336/gm.49.2.07
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1570117489

Abstract

We determine up to isomorphism finite non-Dedekindian p-groups G (i.e., p-groups which possess non-normal subgroups) such that the normal closure of each non-normal cyclic subgroup in G is nonabelian.It turns out that we must have p=2 and G has an abelian maximal subgroup A of exponent 2e, e≥ 3, and an element v G-A such that for all h A we have either hv=h-1 or hv=h -1+2e-1.