  We study a Batalin-Vilkovisky algebra structure on the Hochschild cohomology
of the group ring of finitely generated abelian groups. The Batalin-Vilkovisky
algebra structure for finite abelian groups comes from the fact that the group
ring of finite groups is a symmetric algebra, and the Batalin-Vilkovisky
algebra structure for free abelian groups of finite rank comes from the fact
that its group ring is a Calabi-Yau algebra.
