On units of twisted group algebras

We study units of twisted group algebras. Let G be a finite group and K be a field of characteristic p > 0. Assume that K is not algebraic over a finite field. We determine when units of K^t[G] do not contain any nonabelian free subgroup. We also discuss what will happen when G is locally finite. For twisted group algebras of locally finite groups over any infinite field of characteristic p > 0, we characterize those twisted group algebras with units satisfying a group identity. Finally, we include a new characterization for twisted group algebras to satisfy a polynomial identity.