GROUP-ALGEBRAS WHOSE UNITS SATISFY A GROUP IDENTITY .2.

Let K[G] be the group algebra of a torsion group G over an infinite he ld K, and let U = U(G) denote its group of units. A recent paper of A. Giambruno, S. K. Sehgal, and A. Valenti proved that if U satisfies a group identity, then K[G] satisfies a polynomial identity, thereby con firming a conjecture of Brian Hartley. Here we add a footnote to their result by showing that the commutator subgroup G' of G must have boun ded period. Indeed, this additional fact enables us to obtain necessar y and sufficient conditions for U(G) to satisfy an identity.