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

Let a and b be elements of a group,with a^2=e , b^6=e and a.b=b^4.a find its order and express its inverse in form of a^m.b^n

2. Relevant equations

3. The attempt at a solution

(ab)^2=(ab)(ab)=(ab)(b^4.a)=a(b^5)a

(ab)^3=a(b^5)a(ab)=a(b^5)(a^2)b=a(b^6)=ae=a

it implies(ab)^6=e

thus order(ab) divides 6.It is not 3 hence it is 6.

Help me in solving second part.I can express inverse in form of b^m.a^n but not in the asked form.

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# Homework Help: Group theory finding order of element and inverse

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