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Title: Explicit Brauer induction and the Glauberman correspondence
Author: Case, Adam Martin
ISNI:       0000 0001 3524 5815
Awarding Body: University of Southampton
Current Institution: University of Southampton
Date of Award: 2002
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Let S and G be finite groups of coprime order such that S acts on G. If S is solvable, Glauberman [11] proves the existence of a bijection between the S-fixed irreducible representations of G and the irreducible representations of Gs. In the case of G solvable, Isaacs [13] uses a totally different method to prove the existence of a bijection between the same two sets of representations. Assuming the existence of the Glauberman correspondence, Boltje [5] uses the method of Explicit Brauer Induction (EBI) to give an explicit version of this correspondence for the case in which S is a p-group. After presenting the above results, we outline a strategy for investigating these correspondences using Explicit Brauer Induction, and we use these ideas to give a new proof for the theorems of Glauberman and Boltje. We move on to suggest some ideas of how this work may extend to Isaacs' correspondence. We also mention a link to Shintani's correspondence [25]. In the final chapter, we look at cryptography, and mention a potential application of some of our techniques (Adams Operations) in this field.
Supervisor: Snaith, Victor Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics