Some identities on twisted group algebras

Abstract

Let G be a group and F be a field of characteristic . In this paper we provide some necessary and sufficient conditions for a twisted group algebra to satisfies a non-matrix identity. This allows us to show that a crossed product is Lie nilpotent if and only if σ is trivial, G is nilpotent and p-abelian, G has a unique normal Sylow p-subgroup P and for some central -subgroup Q and is stably untwisted. Also, is Lie nilpotent if and only if is commutative. Some generalized group identities on the unit group of are also investigated.