In the group s3 let r 123s 12e 1a verify that e r r2 s

Question

In the group S₃, let r = (123),s = (12),e = (1).

(a) Verify that {e, r, r², s, rs, r²s} is a complete list of elements of S₃.

(c) Show that with the relations sr = r²s, r³ = e, and s² = e, any product can be evaluated by reducing it to an element in the list under (a)

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