2019-04-17 01:58:44 -0500 | received badge | ● Student (source) |

2019-04-17 01:18:50 -0500 | asked a question | group algebra 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: $$e_0 = \hat{G}$$ $$e_1=\hat{b}−\widehat{(\text{ideal generated by }a)∗ (\text{ideal generated by }b)}$$ $$e_2=\widehat{a−G}$$ $$e_3=\widehat{(\text{ideal generated by }a_p)∗ (\text{ideal generated by }b)}−\hat{G}$$ |

Copyright Sage, 2010. Some rights reserved under creative commons license. Content on this site is licensed under a Creative Commons Attribution Share Alike 3.0 license.