Assume |x| = n and |y| = m. Suppose that xy = yx. Prove that .

What is the commutativity used for?

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- October 8th 2011, 07:56 PMdwsmithLCM[|x|,|y|]
Assume |x| = n and |y| = m. Suppose that xy = yx. Prove that .

What is the commutativity used for? - October 8th 2011, 08:00 PMDevenoRe: LCM[|x|,|y|]
to establish that

by the way, what you are trying to prove is false, without further conditions. consider m = n, and . - October 8th 2011, 08:11 PMdwsmithRe: LCM[|x|,|y|]
- October 8th 2011, 08:18 PMDevenoRe: LCM[|x|,|y|]
my bad...didn't see the extra vertical line. in any case, what you do is show that (xy)^lcm(m,n) = e, and you're done!

- October 9th 2011, 09:46 AMdwsmithRe: LCM[|x|,|y|]
Ok so here is what I have.

But m and n are least so .

So we have

Can I just say k is a common multiple and by definition of LCM, k|LCM? - October 9th 2011, 01:19 PMzoekRe: LCM[|x|,|y|]
- October 9th 2011, 01:27 PMzoekRe: LCM[|x|,|y|]