On some finite 2-groups in which the derived group has two generators
Czechoslovak Mathematical Journal, Tome 73 (2023) no. 1, pp. 71-100
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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 $2^{12}$.
@article{10_21136_CMJ_2022_0415_21,
author = {Benjamin, Elliot and Snyder, Chip},
title = {On some finite 2-groups in which the derived group has two generators},
journal = {Czechoslovak Mathematical Journal},
pages = {71--100},
publisher = {mathdoc},
volume = {73},
number = {1},
year = {2023},
doi = {10.21136/CMJ.2022.0415-21},
mrnumber = {4541090},
zbl = {07655756},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2022.0415-21/}
}
TY - JOUR AU - Benjamin, Elliot AU - Snyder, Chip TI - On some finite 2-groups in which the derived group has two generators JO - Czechoslovak Mathematical Journal PY - 2023 SP - 71 EP - 100 VL - 73 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2022.0415-21/ DO - 10.21136/CMJ.2022.0415-21 LA - en ID - 10_21136_CMJ_2022_0415_21 ER -
%0 Journal Article %A Benjamin, Elliot %A Snyder, Chip %T On some finite 2-groups in which the derived group has two generators %J Czechoslovak Mathematical Journal %D 2023 %P 71-100 %V 73 %N 1 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2022.0415-21/ %R 10.21136/CMJ.2022.0415-21 %G en %F 10_21136_CMJ_2022_0415_21
Benjamin, Elliot; Snyder, Chip. On some finite 2-groups in which the derived group has two generators. Czechoslovak Mathematical Journal, Tome 73 (2023) no. 1, pp. 71-100. doi: 10.21136/CMJ.2022.0415-21
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