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Can anyone help in writing a code to find the list of idempotent and primitive elements of a group algebra, the examples goes like this. Let p be an odd prime such that $\bar2$ generates $U(Z_{p^2})$ and G=(ideal generated by a)∗ (ideal generated by b) an abelian group, with $o(a)=p^2$ and $o(b)=p$. Then $F_2G$ has four inequivalent minimal codes, namely, the ones generated by the idempotents $e_0= \hat{G}$, $e_1=\hat{b}−\hat{(ideal generated by 'a')∗ (ideal generated by 'b')}$(note: its a big hat), $e_2=\hat{a−G}$ and $e_3=\hat{(ideal generated by 'a_p')∗ (ideal generated by 'b')}−\hat{G}$.

Can anyone help in writing a code to find the list of idempotent and primitive elements of a group algebra, the algebra?

The examples goes like this. Let p $p$ be an odd prime such that $\bar2$ generates $U(Z_{p^2})$ and G=(ideal let $G =(\text{ideal generated by a)∗ (ideal }a) ∗ (\text{ideal generated by b) }b)$ an abelian group, with $o(a)=p^2$ and $o(b)=p$. $o(b)=p$.

Then $F_2G$ has four inequivalent minimal codes, namely, the ones generated by the idempotents $e_0= \hat{G}$, $e_1=\hat{b}−\hat{(ideal idempotents:

$$e_0 = \hat{G}$$ $$e_1=\hat{b}−\widehat{(\text{ideal generated by 'a')∗ (ideal }a)∗ (\text{ideal generated by 'b')}$(note: its a big hat), $e_2=\hat{a−G}$ and $e_3=\hat{(ideal }b)}$$ $$e_2=\widehat{a−G}$$ $$e_3=\widehat{(\text{ideal generated by 'a_p')∗ (ideal }a_p)∗ (\text{ideal generated by 'b')}−\hat{G}$.}b)}−\hat{G}$$

Can anyone help in writing code to find the list of idempotent and primitive elements of a group algebra?

The examples goes like this. Let $p$ be an odd prime such that $\bar2$ generates $U(Z_{p^2})$ and let $G =(\text{ideal generated by }a) ∗ (\text{ideal generated by }b)$ an abelian group, with $o(a)=p^2$ and $o(b)=p$.

Then $F_2G$ has four inequivalent minimal codes, namely, the ones generated by the idempotents:

$$e_0 = \hat{G}$$ $$e_1=\hat{b}−\widehat{(\text{ideal generated by }a)∗ (\text{ideal generated by }b)}$$ $$e_2=\widehat{a−G}$$ $$e_3=\widehat{(\text{ideal generated by }a_p)∗ (\text{ideal generated by }b)}−\hat{G}$$