Please all solve the question (4) Let G be a finite abelian group. Let V + {0} be an irreducible CG-module offinite degree.(a)Let he G. WriteTh: 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)- 1What do you exactly need?

Given: In this problem, G is an finite abelian group. V≠{0} is an irreducible ℂG -module of finite…

Answered: (4) Let G be a finite abelian group.…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.4: Cosets Of A Subgroup

Problem 30E: Let G be an abelian group of order 2n, where n is odd. Use Lagranges Theorem to prove that G...

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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.