Generalized Commutativity in Group Algebras We study group algebras $FG$ which can be graded by a finite abelian group $\Gamma$ such that $FG$ is $\beta$-commutative for a skew-symmetric bicharacter $\beta$ on $\Gamma$ with values in $F^*$. Categories:16S34, 16R50, 16U80, 16W10, 16W55