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- W2133923182 abstract "Let S and G be linitc groups such that S acts on G and (IS, ICI) = 1 and let C denote the fixed-point subgroup, C = C,(S). It is well known in this situation that there exists a natural bijection from the set Irr,(G) of S-invariant irreducible characters of G onto Irr( C), the full set of irreducible characters of C. When S is solvable, this bijection was constructed by G. Glauberman [2] and in the remaining case, where G is solvable of odd order, a totally different construction [3] gives the desired character correspondence. It was proved by T. R. Wolf [g] that when both constructions apply, when S is solvable and IG( is odd, the two constructions yield exactly the same map. If 31 E Irr,(G), we write x* E Irr(C) to denote the uniquely determined corresponding character. Similarly, if HE G is S-invariant, and 0 E Irr,(H). we write f3* E Irr(Hn C) to denote the image of 8 under the character bijection induced by the action of S on H. Our main result is the following." @default.
- W2133923182 created "2016-06-24" @default.
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- W2133923182 date "1991-06-01" @default.
- W2133923182 modified "2023-10-18" @default.
- W2133923182 title "Character correspondences and irreducible induction and restriction" @default.
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- W2133923182 doi "https://doi.org/10.1016/0021-8693(91)90150-7" @default.
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