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Problem (Coset Products Of The Automorphisms Of The Square)
You'll need your work from the previous problem to continue with this problem.
- Pick a subgroup $H$ from the previous problem where the indentification graph of $G$ using right cosets of $H$ resulted in a Cayley graph. Compute the set products $(Ha)(Hb)$ for each pair of cosets. Organize your work into a multiplication table. Then repeat this with a different $H$.
- Pick a subgroup $H$ where the identification graph was not a Cayley graph. Compute the set products $(Ha)(Hb)$ for each pair of cosets. Organize your work into a multiplication table.
- Does the set product $(Ha)(Hb)$ always result in another coset of $H$? What did you find?
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