(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The dicyclic group of order 12 is generated by 2 generators x and y such that: ##y^2 = x^3, x^6 = e, y^{-1}xy =x^{-1} ## where the element of Dic 12 can be written in the form ##x^{k}y^{l}, 0 \leq x < 6, y = 0,1##. Write the product between two group elements in the form ##(x^{k}y^{l})(x^{m}y^{n})## and show that ##a^3## is the only order 2 element and ##a^2## is the only order 3 element in Dic12.

2. Relevant equations

##y^2 = x^3, x^6 = e, y^{-1}xy =x^{-1}##

3. The attempt at a solution

The answer I was able to obtain is ##(x^{k}y^{l})(x^{m}y^{n}) = x^{k-m}y^{l+n}## for ##l = -1, 1## and ##(x^{k}y^{l})(x^{m}y^{n}) = x^{k+m}y^{n}## for ##l = 0##. Is this correct? Also, Isn't it that ##a^4## also an order 3 element? So now, I'm confused T_T

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# Homework Help: Dic12 element orders

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