(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.
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...
Related questions
Question
Please all solve the question
![(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?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F005bc346-9e42-4168-a798-92139c4eb6d2%2Fd3fd9411-cbd6-422c-ba27-2e23df99c236%2Fzxqkvqa_processed.jpeg&w=3840&q=75)
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?
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 6 steps
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Recommended textbooks for you
![Elements Of Modern Algebra](https://www.bartleby.com/isbn_cover_images/9781285463230/9781285463230_smallCoverImage.gif)
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
![Elements Of Modern Algebra](https://www.bartleby.com/isbn_cover_images/9781285463230/9781285463230_smallCoverImage.gif)
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,