Finite p-groups all of whose maximal subgroups, except one, have cyclic derived subgroups
Let G be a finite p-group which has exactly one maximal subgroup H such that its derived subgroup H' is noncyclic. Then we must have p = 2, G′ is abelian of rank 2, |G′ : H′| = 2 and d(G) = 2 or 3 (Theorems 6 and 8). This solves the problem No. 2248 stated by Berkovich in [Groups of Prime Power...
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
February 2015
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| In: |
Journal of algebra and its applications
Year: 2015, Volume: 14, Issue: 01 |
| ISSN: | 0219-4988 |
| DOI: | 10.1142/S0219498814500807 |
| Online Access: | Verlag, Volltext: http://dx.doi.org/10.1142/S0219498814500807 Verlag, Volltext: http://www.worldscientific.com/doi/abs/10.1142/S0219498814500807 
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| Author Notes: | Zvonimir Janko |
| Summary: | Let G be a finite p-group which has exactly one maximal subgroup H such that its derived subgroup H' is noncyclic. Then we must have p = 2, G′ is abelian of rank 2, |G′ : H′| = 2 and d(G) = 2 or 3 (Theorems 6 and 8). This solves the problem No. 2248 stated by Berkovich in [Groups of Prime Power Order, Vol. 3 (Walter de Gruyter, Berlin, 2011)]. |
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| Item Description: | Published online: 9 September 2014 Gesehen am 26.02.2018 |
| Physical Description: | Online Resource |
| ISSN: | 0219-4988 |
| DOI: | 10.1142/S0219498814500807 |