Permutation module
= Permutation module
{title2=$R[X]$}
For a finite <group action> on a finite set $X$, $R[X]$ is the free $R$-module with basis $X$, with the group permuting that basis. For a transitive set $G/H$ it is $\operatorname{Ind}_H^G R$. Disjoint unions of sets give <direct sums> of permutation modules.