Hi all ,
Just wanted to see if i was handling this Q correctly
Q in a group G , a^5 = e, aba^-1 = b^2 for some a,b element of G.
find the order of b?
I said aba^-1 = b^2
i) multiplied RHS and LHS by 'a'
to get ab = b^2a
ii) then i) multiplied RHS and LHS by b^-1 (b inverse)
to get a = b^2ab^-1
then put both side to the power of 5
to get a^5 = e
so e = (b^2ab^-1)^5
e = b^10a^5b^-5
e = b^10b^-5 (a^5 turns to e)
so order of b = 5 ??????
Not sure at all if this is correct any suggestions would be great.