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Problem 3.11. Consider Spin1x2 with generating set {$11,S22,512}. (a) Find the Cayley diagram for the subgroup ($11) inside the Cayley diagram for Spin 1x2. Identify all of the clones of ($11) inside Spin1x2. (b) Find the Cayley diagram for the subgroup ($11,822) inside the Cayley diagram of Spin1x2. Identify the clones of ($11,S22) inside Spin1x2. One of the benefits of Cayley diagrams is that they are useful for visualizing sub- groups. However, recall that if we change our set of generators, we might get a very different looking Cayley diagram. The upshot of this is that we may be able to see a sub- group in one Cayley diagram for a given group, but not be able to see it in the Cayley diagram arising from a different generating set. 1 2 + 17 1 2 2|I IN 1 2 1 12 || Figure 2.2 Problem 3.11. Consider Spin1x2 with generating set {$11,S22,512}. (a) Find the Cayley diagram for the subgroup ($11) inside the Cayley diagram for Spin 1x2. Identify all of the clones of ($11) inside Spin1x2. (b) Find the Cayley diagram for the subgroup ($11,822) inside the Cayley diagram of Spin1x2. Identify the clones of ($11,S22) inside Spin1x2. One of the benefits of Cayley diagrams is that they are useful for visualizing sub- groups. However, recall that if we change our set of generators, we might get a very different looking Cayley diagram. The upshot of this is that we may be able to see a sub- group in one Cayley diagram for a given group, but not be able to see it in the Cayley diagram arising from a different generating set. 1 2 + 17 1 2 2|I IN 1 2 1 12 || Figure 2.2

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