Finite 2-groups with exactly one maximal subgroup which is neither abelian nor minimal nonabelian

• Verfasst von: Božikov, Zdravka [VerfasserIn]
• Verfasst von: Janko, Zvonimir [VerfasserIn]
• Titel: Finite 2-groups with exactly one maximal subgroup which is neither abelian nor minimal nonabelian
• Verf.angabe: Zdravka Božikov and Zvonimir Janko
• Jahr: 2010
• Umfang: 21 S.
• Fussnoten: Gesehen am 15.02.2023
• Titel Quelle: Enthalten in: Glasnik matematički
• Ort Quelle: Zagreb : Društvo, 1966
• Jahr Quelle: 2010
• Band/Heft Quelle: 45(2010), Seite 63-83
• ISSN Quelle: 1846-7989
• DOI: doi:10.3336/gm.45.1.06
• Datenträger: Online-Ressource
• Sprache: eng
• K10plus-PPN: 1835732151

Abstract

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.