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Zev Chonoles
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Radical of $F_p[SL(2,p)]]$

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Klim Efremenko
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Radical of $F_p[SL(2,p)]

Let $G=SL(2,p)$. Does anyone know what is the radical of the group algebra $F_p[G]$? Does there exists any book/paper where it is calculated?

By radical here I mean maximal ideal I of $F_p[G]$ such that $I^n=0$