Finite 2-groups with exactly one maximal subgroup which is neither abelian nor minimal nonabelian - Božikov, Zdravka; Janko, Zvonimir (Glasnik matematički, 2010)
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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