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!).