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

Let a,b,c,d be elements of a group G and let ab = c, bc = d, cd = a, da = b. Examine the expression da^2b and first derive an expression for b in powers of a. Then express c and d in powers of a. Show that a^5 = e (identity element)

2. Relevant equations

3. The attempt at a solution

So ive been banging me head against this one for a while now. I feel like its something simple and obvious but i cant figure it out. I have an expression for b:

da^2b = daab = (da)(ab) = bc = d

d^-1*daab=d^-1*d

eaab = e

b = a^-2

I cant figure out c or d, well i should say I have worked out values for c and d but know them to be wrong because I can't show a^5 = e. (and also I have the answers to this question)

Thanks

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# Group Theory (Abstract algebra manipulations)

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