Czechoslovak Mathematical Journal, Vol. 73, No. 1, pp. 71-100, 2023
On some finite 2-groups in which the derived group has two generators
Elliot Benjamin, Chip Snyder
Received November 1, 2021. Published online June 20, 2022.
Abstract: 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 $2^{12}$.
Affiliations: Elliot Benjamin (corresponding author), School of Social and Behavioral Sciences, Capella University, 225 South 6th Street, Minneapolis, MN 55402, USA, e-mail: ben496@prexar.com; Chip Snyder, Department of Mathematics and Statistics, University of Maine, 333 Neville Hall, Orono, ME 04469-5752, USA, e-mail: wsnyder@maine.edu