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(4) Let G be a finite abelian group. Let V {0} be an irreducible CG-module of finite degree. Let heG. Write Th: V→ V Th(v) = h.v. Show that my is an isomorphism of CG-modules. Show that T = A₁ ly for some À, € C. Show that deg(V) – 1.

(4) Let G be a finite abelian group. Let V {0} be an irreducible CG-module of finite degree. Let heG. Write Th: V→ V Th(v) = h.v. Show that my is an isomorphism of CG-modules. Show that T = A₁ ly for some À, € C. Show that deg(V) – 1.

Advanced Engineering Mathematics
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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(4) Let G be a finite abelian group. Let V + {0} be an irreducible CG-module of finite degree. (a) Let he G. Write Th: VV, *A(v) = h v. Show that m is an isomorphism of CG-modules (b) Show that ,= A for some A, EC. Show that deg(V)- 1 What do you exactly need?
Transcribed Image Text:(4) Let G be a finite abelian group. Let V + {0} be an irreducible CG-module of finite degree. (a) Let he G. Write Th: VV, *A(v) = h v. Show that m is an isomorphism of CG-modules (b) Show that ,= A for some A, EC. Show that deg(V)- 1 What do you exactly need?
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