3: Subgroups and Isomorphisms
For the next two sections, it would be useful to have all of the Cayley diagrams we’ve encountered in one place for reference. So, before continuing, gather up the following Cayley diagrams:
- \(\text{Spin}_{1\times 2}\) . There are 3 of these. I drew one for you in Section 2.6 and you discovered two more in Problem 2.6.3 .
- \(S_2\) . See Problem 2.6.5a .
- \(R_4\) . See Problem 2.6.5b .
- \(V_4\) . See Problem 2.6.5c .
- \(D_3\) . There are two of these. See Problem 2.6.5d and Problem 2.6.5e .
- \(S_3\) . See Problem 2.6.5f .
- \(D_4\) . See Problem 2.6.5g .