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• W3041122612 abstract "Let B be a block of a finite group G with defect group D. We prove that the exponent of the center of D is determined by the character table of G. In particular, we show that D is cyclic if and only if B contains a large family of irreducible p-conjugate characters. More generally, for abelian D we obtain an explicit formula for the exponent of D in terms of character values. In small cases even the isomorphism type of D is determined in this situation. Moreover, it can read off from the character table whether |D/D'|=4 where D' denotes the commutator subgroup of D. We also propose a new characterization of nilpotent blocks in terms of the character table." @default.
• W3041122612 created "2020-07-16" @default.
• W3041122612 creator A5066540439 @default.
• W3041122612 date "2020-07-09" @default.
• W3041122612 modified "2023-09-27" @default.
• W3041122612 title "Character tables and defect groups" @default.
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• W3041122612 hasPublicationYear "2020" @default.
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