= Solution
{c}
Let $N=\sum_{g\in G}g$ be the <group norm element>. This is a nonzero vector in the <group algebra> $kG$, and $kN$ is a trivial <submodule> of its left regular <module>. If $kG$ were a <semisimple algebra>, this <submodule> would have a $kG$-linear projection $\pi:kG\to kN$. Write $\pi(1)=cN$. Since $gN=N$ for every $g$, we would have
$$
\pi(N)=\sum_{g\in G}g\pi(1)=|G|cN=0,
$$
whereas a projection onto $kN$ satisfies $\pi(N)=N\ne0$. Thus $\boxed{kG\text{ is not semisimple}}$.
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