I am trying to work out all the subgroups of , the dihedral group, i.e. the symmetry group of the square.
I am not sure how to do this. I know of course they must have order 1,2,4,8, so the only real problem is working out the subgroups of order 4. Is there a quick way to do this? Thanks for any help with this
Never seen that notation for a group before although I am aware of the rotations and reflections. Thanks for clarifying.
I know there is an obvious subgroup of order 4 where you take the subgroup of rotations, but how can I work out there are only TWO other subgroups of order 4 and what they are exactly?
You've never seen a group written out in terms of its elements?
How do you usually think of groups? For some groups such as this one, you can get some stuff done by thinking abstractly/geometrically about the group. But how can you REALLY work with a group without being able to write down what is IN the group?