Formula_14977

\[\begin{gathered}\sum_{g \in G} \alpha_{g} t_{g}+\sum_{g \in G} \beta_{g} t_{g}=\sum_{g \in G}\left(\alpha_{g}+\beta_{g}\right) t_{g} ; \\\left(\sum_{g \in G} \alpha_{g} t_{g}\right)\left(\sum_{g \in G} \beta_{g} t_{g}\right)= \\=\sum_{h \in G}\left(\sum_{x y=h, x, y \in G}\left(\alpha_{x} \beta_{y}^{x \sigma} \rho_{x, y}\right)\right) t_{h} .\end{gathered}\]