Question

Suppose a and b are group elements such that |a|=2, b does not equal e, and aba=b^2. Determine |b|.

Answer 1

i am going to guess it is 2

Answer 2

you can prove that \(b^2=b^4\)

Answer 3

which of course means since \(b^4=b^2b^2\) you have \(b^2=b^2b^2\) making \(b^2=e\)
you need some help showing that \(b^2=b^4?\)

Answer 4

Can you explain it a little further? I'm not sure that I follow you. I'm sorry