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Inverse Glauberman–Isaacs correspondence and subnormal subgroups
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Alexandre Turull
Veröffentlicht/Copyright:
8. Januar 2016
Abstract
Let A be a finite group acting on a finite group G with (|A|,|G|) = 1. The Glauberman–Isaacs correspondence is often viewed as providing for each pair of subgroups B1 ⊴ B2 of A a bijection IrrB2(CG(B1)) → Irr(CG(B2)), where IrrB2(CG(B1)) is the set of all irreducible characters of CG(B1) which are invariant under B2. The inverse Glauberman–Isaacs correspondence can be viewed as providing an injective map Irr(CG(B2)) → Irr(CG(B1)). We show that this can naturally be extended to give a corresponding map for each B1 a subnormal subgroup of B2, where B2 is any subgroup of A. The properties of this correspondence are very close to those of the original one.
Received: 2015-2-16
Published Online: 2016-1-8
Published in Print: 2016-3-1
© 2016 by De Gruyter
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Artikel in diesem Heft
- Frontmatter
- Mapping tori of free group automorphisms, and the Bieri–Neumann–Strebel invariant of graphs of groups
- Residual properties of graph products of groups
- On hereditarily just infinite profinite groups obtained via iterated wreath products
- Weak commutativity between two isomorphic polycyclic groups
- Isomorphisms and automorphisms of extensions of bilinear dimensional dual hyperovals and quadratic APN functions
- Finite groups in which pronormality and 𝔉-pronormality coincide
- Towards Thompson's conjecture for alternating and symmetric groups
- Minimal length factorizations of finite simple groups of Lie type by unipotent Sylow subgroups
- A criterion for a finite permutation group to be transitive
- Inverse Glauberman–Isaacs correspondence and subnormal subgroups
Artikel in diesem Heft
- Frontmatter
- Mapping tori of free group automorphisms, and the Bieri–Neumann–Strebel invariant of graphs of groups
- Residual properties of graph products of groups
- On hereditarily just infinite profinite groups obtained via iterated wreath products
- Weak commutativity between two isomorphic polycyclic groups
- Isomorphisms and automorphisms of extensions of bilinear dimensional dual hyperovals and quadratic APN functions
- Finite groups in which pronormality and 𝔉-pronormality coincide
- Towards Thompson's conjecture for alternating and symmetric groups
- Minimal length factorizations of finite simple groups of Lie type by unipotent Sylow subgroups
- A criterion for a finite permutation group to be transitive
- Inverse Glauberman–Isaacs correspondence and subnormal subgroups
