Finite p-groups in which the normal closure of each non-normal cyclic subgroup is nonabelian
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...
Gespeichert in:
| 1. Verfasser: | |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
December 2014
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| In: |
Glasnik matematički
Year: 2014, Jahrgang: 49, Heft: 2, Pages: 333-336 |
| ISSN: | 1846-7989 |
| DOI: | 10.3336/gm.49.2.07 |
| Online-Zugang: | Verlag, Volltext: http://dx.doi.org/10.3336/gm.49.2.07 Verlag, Volltext: https://hrcak.srce.hr/index.php?show=clanak&id_clanak_jezik=193363 
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| Verfasserangaben: | Zvonimir Janko |
MARC
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| 520 | |a 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. | ||
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