|x| = order of x
Assume |x|=n and |y|=m. Suppose that x and y commute: xy = yx. Prove that |xy| divides the least common multiple of m and n.
Can anyone help?
Remark: here are three related questions: suppose G is an abelian group and
Q1: show that it's possible to have (by giving an example!)
Q2: what can we say about if ?
and a much more interesting question:
Q3: show that G has an element of order