Permutation multiplication of non-disjoint cycles in $S_4$

Question

I am having an issue with calculating the product of permutation cycles for calculating commutators.

Consider $A_4$ and the commutator $[(123),(14)(23)]$

So we have $[(123),(14)(23)] = (132)(14)(23)(123)(14)(23)$

I think am calculating incorrectly after checking with an online permutation calculator. The result (using the online permutation calculator) I end up with is $[(123),(14)(23)] = (132)(14)(23)(123)(14)(23) = (12)(34)$

I am getting

$(132)\circ(14)(23)\circ (123)\circ (14)(23) = (13)(24)$

score 2 · Accepted Answer · answered Feb 29 '16 at 06:17

2

Your calculations are correct. Why do you believe your result should be different?

answered Feb 29 '16 at 06:17

Quinn Greicius

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okay that is a relief, I was using wolfram and another online permutation calculator to check and they both gave me $(12)(34)$ – oliverjones Feb 29 '16 at 06:18
I think the calculator might be confusing the order of the composition, if you used something like this: http://www.bananattack.com/permutations/ – Quinn Greicius Feb 29 '16 at 06:35
Yep, that's exactly what I used. – oliverjones Mar 01 '16 at 01:46

Permutation multiplication of non-disjoint cycles in $S_4$

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