over divisible field...

把这道题涉及的内容放一起：HW15

下面这个例子也挺有意思的

Assume that $k$ has characteristic $p$ dividing the order of $G$, then the line $k(SG)=\mathrm{span}\{{\sum }_{g\in G}g\}$ has no $G$-stable complement in the regular representation of $G$.

Link to original