Titlebook: Characters and Blocks of Solvable Groups; A User’s Guide to La James Cossey,Yong Yang Book 2024 The Editor(s) (if applicable) and The Autho

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Base SizesIf . acts on a set ., a base for the action is defined to be a set of elements of . whose centralizers in . intersect trivially. The focus in this chapter is to prove a number of results, mostly by Seress and Espuelas, that give minimal base sizes for a number of different types of solvable group actions.

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The Fixed Point Subspace of an Elemented-point subspaces than we proved in earlier chapters. We then use these improved bounds in the discussion of Dolfi’s powerful result, which shows if . is solvable and acts coprimely on . via automorphisms, then there are two elements of . whose centralizers in . intersect trivially. This proof draw

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Huppert’s , Conjectureable group .. We begin with a subtle variation of Gluck’s permutation lemma, and then use another large orbit theorem to prove the best currently known bound for Huppert’s conjecture for solvable groups.

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Other Applications of Large Orbit Theoremsscussing certain induction and restriction theorems that require a variation of Dolfi’s large orbit theorem from Chapter 8. We then discuss a result of Moreto and Wolf that determines that number of characters needed to “cover” the order of the solvable group .. In the last section we discuss, witho

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