Hi there,

I'm going over some past papers for an exam but with no answers and have come a cropper on this one, any help appreciated!

Let be a subgroup of a group and let . Define

i) Prove that is a subgroup of .

ii) Let . Which of these statements is true

Give a proof of the statement that is always true

iii) Set . Prove that and that is a subgroup of that is contained in .

Pretty stuck except for ii) is obviously the right one (I hope!).