Glasnik matematički, Vol. 45 No. 1, 2010.
Original scientific paper
https://doi.org/10.3336/gm.45.1.06
Finite 2-groups with exactly one maximal subgroup which is neither abelian nor minimal nonabelian
Zdravka Božikov
; Faculty of Civil Engineering and Architecture, University of Split, 21000 Split, Croatia
Zvonimir Janko
; Mathematical Institute, University of Heidelberg, 69120 Heidelberg, Germany
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.
Keywords
Minimal nonabelian 2-groups; central products; metacyclic groups; Frattini subgroups; generators and relations
Hrčak ID:
52368
URI
Publication date:
17.5.2010.
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