Composition factors of monodromy groups

By Daniel Frohardt, Kay Magaard. 2001

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Expander graphs, gonality, and variation of Galois representations (2010, unknown): “For instance, if such a graph is associated to a finitely generated group Γ acting on a finite set S, what can one say about the composition factors of the image of Γ in Aut(S)? (Such structure results are known for covers (Ui) with bounded genus, in the work of Guralnick [31] and Frohardt-Magaard [”
Fixed point ratios in actions of finite classical groups, III (2007, background): “This was finally established in [13] and [21], with bounds on fixed point ratios playing a key role in the proof (see [12] and [21, 1.”
Elliptic Subfields and Automorphisms of Genus 2 Function Fields (2001, unknown): “ence τ 3 = σ 4. Thus all σ i can be expressed in terms of τ and σ := σ1: σ1 = σ, σ2 = στ, σ3 = στ 2, σ 4 = τ 3, σ 5 = (στ −1)3 (22) Passing from (σ,τ ρ) to (σ1,...,σ5) is a case of ”translation”, see [14] and [22]. Recall that the index Ind(π) of π ∈ S n is deﬁned as n minus the number of orbits of ”