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RESEARCH PRODUCT

Induction and Character Correspondences in Groups of Odd Order

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Abstract Let P be a Sylow p -subgroup of G . By Irr p ′ ( G ), we denote the set of irreducible characters of G which have degree not divisible by p . When G is a solvable group of odd order, M. Isaacs constructed a natural one-to-one correspondence *:Irr p ′ ( G ) → Irr p ′ ( N G ( P )) which depends only on G and P . In this paper, we show that if ξ G  = χ ∈ Irr p ′ ( G ), then (ξ*) N G ( P )  = χ*.