PreprintOn a certain Lie algebra defined by a finite groupArjeh M. Cohen and D. E. TaylorAbstractFollowing W. Plesken, let G be a finite group and let L(G) denote the Lie subalgebra of the complex group algebra of G spanned by the elements g  g^{1} where g belongs to G. The Lie product is [a,b] = abba. In this paper we determine the structure of L(G). In particular, with two exceptions, L(G) is simple if and only if G is an extraspecial 2group.Keywords: finite group, Lie algebra, SchurFrobenius indicator. AMS Subject Classification: Primary 20.
