= Group norm element
{title2=$N_G=\sum_{g\in G}g$}
The group norm element in the <group algebra> $kG$ is $N_G=\sum_{g\in G}g$. It spans the invariant subspace of the left regular <group representation>, and $N_G^2=|G|N_G$. If the <characteristic> divides $|G|$, a projection from $kG$ onto $kN_G$ would send $N_G$ to both itself and zero, proving that $kG$ is not a <semisimple algebra>. Its action on indecomposable modules is described by <group norm element detects the trivial projective cover>.
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