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1) Draw a Cayley digraph for S3. Hint: what is a set of generators? 2) The...

1) Draw a Cayley digraph for S3. Hint: what is a set of generators?

2) The left cosets of the subgroup h4i of Z12 and left cosets of subgroup h(1, 2, 3)i of S3.

3) Prove or disprove: every group of order 4 is isomorphic to Z4 (hint: use direct products).

4) Show that the set H = {σ ∈ S4 | σ(3) = 3} is a subgroup of S4.

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