Laurent polynomial identities on symmetric units of group algebras

Let F be an infinite field of characteristic p not equal 2, G be a group, and ** be an involution of G extended linearly to an involution of the group algebra FG. In the literature, group identities on units U(FG) and on symmetric units U+(FG) = {alpha is an element of U(FG) divided by divided by alpha(& lowast; )= alpha} have been considered. Here, we investigate normalized Laurent polynomial identities (as a generalization of group identities) on U+(FG) under the conditions that either p > 2 or F is algebraically closed. For instance, we show that if G is torsion and U+(FG) satisfies a normalized Laurent polynomial identity, then U+(FG) satisfies a group identity and FG satisfies a polynomial identity.