Finite p-groups of exponent pe all of whose cyclic subgroups of order pe are normal
Here we classify finite nonabelian p-groups G of exponent pe, e≥2, all of whose cyclic subgroups of order pe are normal in G. Let G0 be the subgroup of G generated by all elements of order pe. If p>2, then G0=G and G is of class 2 (Theorem 1). However if p=2, then |G:G0|≤2 and in case |G:G0|=2 th...
Gespeichert in:
| 1. Verfasser: | |
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| Dokumenttyp: | Article (Journal) |
| Sprache: | Englisch |
| Veröffentlicht: |
15 July 2014
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| In: |
Journal of algebra
Year: 2014, Jahrgang: 416, Pages: 274-286 |
| ISSN: | 1090-266X |
| DOI: | 10.1016/j.jalgebra.2014.05.027 |
| Online-Zugang: | Verlag, Volltext: http://dx.doi.org/10.1016/j.jalgebra.2014.05.027 Verlag, Volltext: http://www.sciencedirect.com/science/article/pii/S0021869314003068 
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| Verfasserangaben: | Zvonimir Janko |
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| 520 | |a Here we classify finite nonabelian p-groups G of exponent pe, e≥2, all of whose cyclic subgroups of order pe are normal in G. Let G0 be the subgroup of G generated by all elements of order pe. If p>2, then G0=G and G is of class 2 (Theorem 1). However if p=2, then |G:G0|≤2 and in case |G:G0|=2 the structure of G is more complicated (Theorems 3, 4 and 5). | ||
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