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Problem (Cayley Graphs Of External Direct Products Of Cyclic Groups)

Please complete the following: (Don't let the different notation $G\times H$ and $G\oplus H$ throw you off. They mean the exact same thing.)

  1. Draw the Cayley graph of $\mathbb{Z}_2\times\mathbb{Z}_2$ using the generating set $S=\{(1,0), (0,1)\}$.
  2. Draw the Cayley graph of $\mathbb{Z}_2\times\mathbb{Z}_3$ using the generating set $S=\{(1,0), (0,1)\}$.
  3. Draw the Cayley graph of $\mathbb{Z}_2\oplus\mathbb{Z}_5$ using the generating set $S=\{(1,0), (0,1)\}$.
  4. Draw the Cayley graph of $\mathbb{Z}_3\oplus\mathbb{Z}_5$ using the generating set $S=\{(1,0), (0,1)\}$.
  5. Draw the Cayley graph of $\mathbb{Z}_2\times\mathbb{Z}_3\times\mathbb{Z}_5$ using the generating set $S=\{(1,0,0), (0,1,0),(0,0,1)\}$.
  6. Draw the Cayley graph of $U(15)$ using the generating set $S=\{7,11\}$. Which graph above does this look like?

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