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I've read that the radical layers of the group algebra $kP$ of a $p$-group $P$ coincides with the its socle layers (char $k = p$). What does this tell me about the structure of the group algebra or resp. about p-groups?

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    «To understand how kP-modules glue together» is 87% of what representation theory is! That is not a specific question, really :)2011-11-30

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