Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 2002 • Question 7

Question

Math 6310 • Algebra Fall 2002 • Question 7

Let \(G\) be a finite group, and let \(C\) be the category of finitely generated \(\mathbb {Q}[G]\)-modules. Show the the functor which takes a \(\mathbb {Q}[G]\)-module to its submodule of invariants (that is, the set of \(m\in M\) such that \(gm=m\) for all \(g\in G\)) is exact.

Raw LaTeX

Let \(G\) be a finite group, and let \(C\) be the category of finitely generated \(\mathbb{Q}[G]\)-modules.
Show the the functor which takes a \(\mathbb{Q}[G]\)-module to its submodule of invariants (that
is, the set of \(m\in M\) such that \(gm=m\) for all \(g\in G\)) is exact.

Topic Tags

Exact Sequences of Modules Ext Functors and Module Extensions Finite Group Theory Hom Functors and Module Homomorphisms