@article{Aseeri2026, 
author = {Fawaz Aseeri and Julian Kaspczyk},
title = {On generalized quaternion Sylow    2-subgroups and    2-nilpotence of finite groups},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {5},
pages = {14757-14762},
keywords = {finite group, p-nilpotent, Sylow 2-subgroup, quaternion group, p-constrained},
url = {https://www.sciopen.com/article/10.3934/math.2026606},
doi = {10.3934/math.2026606},
abstract = {In 2020, Mousavi proved that a finite group    G with a generalized quaternion Sylow    2-subgroup    S is    2-nilpotent if    3  ∤      |    G      |   or if    G is solvable and        |    S      |    >  16. In this note, we generalized the result of Mousavi and provided a simpler proof. In detail, we showed that a finite group with a generalized quaternion Sylow    2-subgroup is    2-nilpotent if, and only if, it is        S          L      2        (    3    )  -free and that, for a finite group with a generalized quaterion Sylow    2-subgroup of order strictly greater than    16, the properties of being    2-nilpotent, solvable, and    2-constrained are equivalent.}
}