Point groups and symmetry: Adding and subtracting operations

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SUMMARY

The discussion focuses on the operations of point groups and symmetry in inorganic chemistry, specifically addressing the addition and subtraction of symmetry operations. The examples provided include C3 – S56, S4 + i, and C3 + i, illustrating the need to generate new groups by combining existing elements with new ones. The key takeaway is that when a new element is added to a group, the resulting group consists of all possible combinations of the new element with the existing operations. This process can be complex and requires careful consideration of the interactions between the elements.

PREREQUISITES
  • Understanding of point groups in symmetry operations
  • Familiarity with symmetry elements such as C3, S4, and i
  • Basic knowledge of group theory in chemistry
  • Ability to perform operations on mathematical groups
NEXT STEPS
  • Study the properties of symmetry operations in point groups
  • Learn about group theory applications in inorganic chemistry
  • Explore the concept of generating sets in group theory
  • Practice problems involving the addition and subtraction of symmetry operations
USEFUL FOR

Students in inorganic chemistry, particularly those studying symmetry and group theory, as well as educators looking to enhance their understanding of point groups and symmetry operations.

Jormungandr
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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!
 
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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.
 

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