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...
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| Main Author: | |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
December 2014
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| In: |
Glasnik matematički
Year: 2014, Volume: 49, Issue: 2, Pages: 333-336 |
| ISSN: | 1846-7989 |
| DOI: | 10.3336/gm.49.2.07 |
| Online Access: | 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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| Author Notes: | Zvonimir Janko |
| Summary: | 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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| Item Description: | Gesehen am 22.02.2018 |
| Physical Description: | Online Resource |
| ISSN: | 1846-7989 |
| DOI: | 10.3336/gm.49.2.07 |