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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 1999 • Question 8

Question

Math 6310 • Algebra Fall 1999 • Question 8

Let \(G\) be a finite group. Prove that every short exact sequence of \(\mathbb {C}[G]\)-modules splits, where \(\mathbb {C}[G]\) is the group algebra of \(G\) over the complex numbers.

Raw LaTeX

Let \(G\) be a finite group. Prove that every short exact sequence of \(\mathbb{C}[G]\)-modules
splits, where \(\mathbb{C}[G]\) is the group algebra of \(G\) over the complex numbers.

Topic Tags

Exact Sequences of Modules Finite Group Theory Representation Theory