On some finite 2-groups in which the derived group has two generators

Benjamin, Elliot, and Snyder, Chip. "On some finite 2-groups in which the derived group has two generators." Czechoslovak Mathematical Journal 73.1 (2023): 71-100. <http://eudml.org/doc/299354>.

@article{Benjamin2023,
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 $2^\{12\}$.},
author = {Benjamin, Elliot, Snyder, Chip},
journal = {Czechoslovak Mathematical Journal},
keywords = {2-group; metabelian},
language = {eng},
number = {1},
pages = {71-100},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On some finite 2-groups in which the derived group has two generators},
url = {http://eudml.org/doc/299354},
volume = {73},
year = {2023},
}

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
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 73
IS - 1
SP - 71
EP - 100
AB - 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 $2^{12}$.
LA - eng
KW - 2-group; metabelian
UR - http://eudml.org/doc/299354
ER -