Talk:2.2.20/@comment-71.232.156.126-20120605193232

Here's an idea for part b. We know at the outset that we'll need the following:

1. a nonabelian group

2. two different elements, each of finite order

3. neither one of the elements in 2 can be the identity (why?)

Nonabelian, of course, makes us think of matrices. Furthermore, we've already seen a 2x2 matrix that has finite order but isn't the identity: think back to problem 2.2.1.

Now that we have one element, can you modify the matrix in 2.2.1 to get another element, also of finite order, so that the product of our two elements does not have finite order?