Group algebras whith symmetric units satisfying a group identity

We study group algebras FG for which the symmetric units under the natural involution: g∗ = g−1 satisfy a group identity. For infinite fields F of characteristic ≠ 2, a classification of torsion groups G whose symmetric units) satisfy a group identity was given by Giambruno-Sehgal-Valenti. We extend this work to non torsion groups.