Point groups and symmetry: Adding and subtracting operations

[Jormungandr]

Homework Statement

I haven't been assigned these questions, but I'm trying to trudge through them to better understand symmetry. This is for my inorganic class.

It's just a series of short questions like:

C₃ – S⁵₆ = ?
S₄ + i = ?
C₃ + i = ?

Stuff like this. And just looking at the elements in each group doesn't really help, because it's not just the given operation that's added, but sometimes several operations get added. I know the answer to each of these, but it's not really intuitive and I could use some help trying to think through them. Help is appreciated. Thanks!

 

[BruceW]

well yes, you're right. when an extra element is added to the group, they really mean that the new group is all the elements that can be generated, by using the new element with old elements in the group. For example, in the case "C₃ + i" to find out what the new group is, you need to find all the different ways to combine the new element with the old group. It's not too difficult in this specific case. But you're right that in general, it can be non-intuitive and require quite a lot of work.