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)

= b^5

so order of b = 5 ??????

Not sure at all if this is correct any suggestions would be great.

thanks

chave