> > There is certainly a much smaller number than 26!. The order of an element > > in the symmetric group is the LCM of its cycle lengths. For QWERTY->DVORAK > > I get the cycle decomposition of > > > > (Q ' - [ / Z ; S O R P L N B X) (W ,) (E . V K T Y F U G I C J H D) (A) (M) > > That's what I was curious about. Did you sit down and map it? I guess > there was nothing on T.V. Don't know what I might have missed on TV...Buffy's mom die again? I found a chart on the web showing QWERTY and Dvorak side by side, then it just took a minute to write down the permutation as cycles--that's hardly a computation, just a different way of writing it down. A concrete example seemed better than a theorem. My real point was just that permutations have small orders relative to the order of the group and you can compute them quite easily. -- Al