ok ive managed to solve the other 2 questions.

here is my final one:

(1)

If G is a group and , define G(n) = { x E G: ord(x) = n}

(2)

If show that, for all , |G(n)| = |H(n)|.

(3)

Deduce that, is not .

Is it true that

Is it true that

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