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- W2330873845 abstract "Abstract Let G be a finite π-separable group, where π is a set of primes. The π-partial characters of G are the restrictions of the ordinary characters to the set of π -elements of G. Such an object is said to be irreducible if it is not the sum of two nonzero partial characters and the set of irreducible π- partial characters of G is denoted I π ( G ). (If p is a prime and π = p ′ , then I π ( G ) is exactly the set of irreducible Brauer characters at p .) From their definition, it is obvious that each partial character φ ∊ I π ( G ) can be “lifted” to an ordinary character χ ∊ Irr( G ). (This means that φ is the restriction of χ to the π-elements of G .) In fact, there is a known set of canonical lifts B π ( G ) ⊆ Irr( G ) for the irreducible π-partial characters. In this paper, it is proved that if 2 ∉ π, then there is an alternative set of canonical lifts (denoted D π ( G )) that behaves better with respect to character induction. An application of this theory to M-groups is presented. If G is an M-group and S ⊆ G is a subnormal subgroup, consider a primitive character θ ⊆ Irr( S ). It was known previously that if | G : S | is odd, then θ must be linear. It is proved here without restriction on the index of S that θ (1) is a power of 2." @default.
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- W2330873845 date "1996-12-01" @default.
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- W2330873845 title "Induction and Restriction of π-Partial Characters and their Lifts" @default.
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- W2330873845 doi "https://doi.org/10.4153/cjm-1996-064-9" @default.
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