(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
Expert Solution
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
Recommended textbooks for you
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,
Elements Of Modern Algebra
Algebra
ISBN:
9781285463230
Author:
Gilbert, Linda, Jimmie
Publisher:
Cengage Learning,