ok ive managed to solve the other 2 questions.

here is my final one:

(1)

If G is a group and $\displaystyle n \geq 1 $, define G(n) = { x E G: ord(x) = n}

(2)

If $\displaystyle G \cong H $ show that, for all $\displaystyle n \geq 1 $, |G(n)| = |H(n)|.

(3)

Deduce that, $\displaystyle C_3 X C_3$ is not $\displaystyle \cong C_9$.

Is it true that $\displaystyle C_3 X C_5 \cong C_15$

Is it true that $\displaystyle C_2 X C_6 \cong C_12$

What is going on here?

any help to get me started is highly appreciated. ill attempt the questions as usual once i have some idea of what to do. thnx so much