BV structure on Hochschild cohomology of the group ring of quaternion group of order eight in characteristic two

Let k   be an algebraically closed field of characteristic two and let Q8Q8 be the quaternion group of order 8. We determine the Gerstenhaber Lie algebra structure and the Batalin–Vilkovisky structure on the Hochschild cohomology ring of the group algebra kQ8kQ8.