Finite 2-groups with exactly one maximal subgroup which is neither abelian nor minimal nonabelian
We shall determine the title groups G up to isomorphism. This solves the problem Nr.861 for p = 2 stated by Y. Berkovich in [2]. The resulting groups will be presented in terms of generators and relations. We begin with the case d(G) = 2 and then we determine such groups for d(G) > 2. In these th...
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| Main Authors: | , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
2010
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| In: |
Glasnik matematički
Year: 2010, Volume: 45, Pages: 63-83 |
| ISSN: | 1846-7989 |
| DOI: | 10.3336/gm.45.1.06 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.3336/gm.45.1.06 Verlag, lizenzpflichtig, Volltext: http://web.math.hr/glasnik/EasyTracker.php?id=45106 
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| Author Notes: | Zdravka Božikov and Zvonimir Janko |
| Summary: | We shall determine the title groups G up to isomorphism. This solves the problem Nr.861 for p = 2 stated by Y. Berkovich in [2]. The resulting groups will be presented in terms of generators and relations. We begin with the case d(G) = 2 and then we determine such groups for d(G) > 2. In these theorems we shall also describe all important characteristic subgroups so that it will be clear that groups appearing in distinct theorems are non-isomorphic. Conversely, it is easy to check that all groups given in these theorems possess exactly one maximal subgroup which is neither abelian nor minimal nonabelian. |
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| Item Description: | Gesehen am 15.02.2023 |
| Physical Description: | Online Resource |
| ISSN: | 1846-7989 |
| DOI: | 10.3336/gm.45.1.06 |