Here is the problem concerning permutation groups:(adsbygoogle = window.adsbygoogle || []).push({});

u =

1 2 3 4

-------

3 4 2 1

Show that there is no p such that p^2 (the second permutation) = u

I've tried just substituting values for p1, p2, p3 and p4 in:

1 2 3 4

------------

p1 p2 p3 p4

p1 = 1 doesn't work because 1 would never go to 3 the second time

p1 = 2, p2 = 3, p3 = 4, p4 = 2, which doesn't work because 4 doesn't go to 1 the second time, it goes to 3.

p1 = 3 doesn't work because then p3 would also have to be 3, so 3 wouldn't go to 2 the second time

p1 = 4, p2 = 1, p3 = 1, p4 = 3, which doesn't work because 3 goes to 4 instead of the required 2.

Is this sufficient to show what's being asked?

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# Homework Help: Problem concerning permutation groups

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