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

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