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

https://hrcak.srce.hr/52368

Publication date:

17.5.2010.

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