ABSTRACT
We remark that in Hartley's conjecture, the hypothesis of G being torsion cannot be removed since in general we cannot expect that a group identity on U(FG) forces FG to satisfy a polynomial identity. In fact if G is a torsion free nilpotent group, then G can be ordered and, by [22, Proposition 1.6], [/(FG) has only trivial units i.e., [/(FG) = F* x G. It follows that [/(FG) satisfies a group identity but, in view of the above characterization of group algebras satisfying
a polynomial identity, it is easy to see that FG does not necessarily satisfy a polynomial identity.
