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Some remarks on Dade’s conjecture. (English) Zbl 0927.20006
Summary: We prove some results concerning Dade’s conjecture. First we prove that for every finite group \(G\) with \(O_p(G)=1\) for \(d=1\) the ordinary and invariant conjectures are true. Later we consider the connection of the ordinary and the projective conjectures for groups having Schur multiplier of prime order. In the end we show by some examples that the analogue of Brauer’s first main theorem and that of the Alperin-McKay conjecture are not true in general for chain normalizers.

MSC:
20C20 Modular representations and characters
20C15 Ordinary representations and characters
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