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Summary: B7 Symmetry 2009-10: Questions
1. Using the definition of a group, prove the Rearrangement Theorem, that the set of h products RS
obtained for a fixed element S, when R ranges over the h elements of the group, comprises each
element of the group exactly once.
2. Find the equivalence classes of the point group D4h by collecting together symmetry operations
that are related by symmetry. How many distinct classes of C2 operation are there?
3. Show that the representation matrices generated by
R i
=
j
j
D ji
R
satisfy D(R)D(S) = D(RS). Demonstrate that these matrices form a group.
Consider secondly the alternative definition
R i
=
j
Dij
R j
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