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Principal blocks and p -radical groups

Xiaohan HuJiwen Zeng — 2016

Czechoslovak Mathematical Journal

Let G be a finite group and k a field of characteristic p > 0 . In this paper, we obtain several equivalent conditions to determine whether the principal block B 0 of a finite p -solvable group G is p -radical, which means that B 0 has the property that e 0 ( k P ) G is semisimple as a k G -module, where P is a Sylow p -subgroup of G , k P is the trivial k P -module, ( k P ) G is the induced module, and e 0 is the block idempotent of B 0 . We also give the complete classification of a finite p -solvable group G which has not more than three...

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