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?
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?