Groups ${\Gamma }_n^4$: algebraic properties

Abstract

In the paper, groups ${\Gamma }_n^4$ closely connected with braid groups are researched from algebraic point of view. More exactly, for $n⩾7$, it is proved that ${\Gamma }_n^4$ is a nilpotent finite $2$-group with $4$-torsion and that its subgroup $({\Gamma }_n^4{)}^{\prime }$ is central.