Got a tricky question here that I'm not too sure how to approach:
is a group of order 12 under multiplication and with the neutral element.
i) is the set of self inverse elements of .
I need to show that is a subgroup of if is abelian.
ii) We now need to assume that is cyclic, with generator and find the order and all the elements of
iii) Give an example of a group of order 12 for which isn't a subgroup. (For this one obviously you need to use the sub-group criteria, just not sure how to apply them).
Greatly appreciate any help/pointers with this.
Thanks in advance