- #1
Bashyboy
- 1,421
- 5
Homework Statement
I am asked to offer an example of two commuting elements whose product does not have an order equal to the least common multiple of their individual orders.
Homework Equations
The Attempt at a Solution
Consider ##-1## and ##1## in ##\mathbb{Z}##. Then ##1+(-1) = 0## which has an order of ##1##, but the order of ##-1## and ##1## is infinity.
Would this be an acceptable answer? I find it unsettling for some reason, but I cannot see anything wrong with it.