Skew-Symmetric Elements of Rational Group Algebras

Abstract

Let $RG$ be the group ring of a finite group $G$ over a commutative ring $R$ with $1$. An element $x$ in $RG$ is said to be skew-symmetric with respect to an involution $\sigma$ of $RG$ if $\sigma (x)=-x.$ A structure theorem for the skew-symmetric elements of $FG$ is given where $F$ is an algebraic extension of $\mathbb{Q}$ which generalizes some previously known results in this direction.

Main result generalized from $\mathbb{Q}G$ to $FG$ where $F$ is an algebraic extension of $\mathbb{Q}$. Major changes in the exposition done. 12 pages