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

Craig