(1) Let G := S4. Then G naturally acts on A := {1, 2, 3, 4}. Let X := { ƒ: A → A} be the set of maps from A to itself. (a) (b) Show that gf := gf g¹ for ge G, f e X defines a G-action on X. Let t: A→A be the map defined by t(i) = 1 for every i E A. Compute the stabilizer G₁ = {g € G|g⋅ t = t} of t.
(1) Let G := S4. Then G naturally acts on A := {1, 2, 3, 4}. Let X := { ƒ: A → A} be the set of maps from A to itself. (a) (b) Show that gf := gf g¹ for ge G, f e X defines a G-action on X. Let t: A→A be the map defined by t(i) = 1 for every i E A. Compute the stabilizer G₁ = {g € G|g⋅ t = t} of t.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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