Group Identities on Units of Group Algebras,

Let U be the group of units of the group algebra FG of a group G over a field F. Suppose that either F is infinite or G has an element of infinite order. We characterize groups G so that U satisfies a group identity. Under the assumption that G modulo the torsion elements is nilpotent this gives a complete classification of such groups. For torsion groups this problem has already been settled in recent years.