Real Quadratic Number Fields with 2-Class Group of Type (2,2).
On some finite 2-groups in which the derived group has two generators
We show that any finite 2-group, whose abelianization has either 4-rank at most 2 or 8-rank 0 and whose commutator subgroup is generated by two elements, is metabelian. We also prove that the minimal order of any 2-group with nonabelian commutator subgroup of 2-rank 2 is .
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