Some Basic Algebra with Exercises: Part 2.

In our previous story we have looked at the Index Theorem and the very often referred Lagrange Theorem:

This shall be the hint for our next exercise.

Exercise:

Solution:

Next let us prove the opposite direction. Here it is where Lagrange’s Theorem comes into play.

The Lagrange Theorem, although very easy to prove, has a large impact on many areas in Algebra and Algebraic Number Theory.

Thank you for reading!