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Consider the equivalence relation in Theorem 9.2. Find the equivalence classes and a

Chapter 9, Problem 9.19

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QUESTION:

Consider the equivalence relation in Theorem 9.2. Find the equivalence classes and a completeset of equivalence class representatives in each of the following special cases.(a) S = {I, 2, ... , n} and G = S".(b) S = {I, 2, 3, 4) and G = (Ci), (2 3)}.(c) S={I, 2, 3, 4, 5}andG={(I),(1 2),(1 3),(23),(123),(13 2)}.

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QUESTION:

Consider the equivalence relation in Theorem 9.2. Find the equivalence classes and a completeset of equivalence class representatives in each of the following special cases.(a) S = {I, 2, ... , n} and G = S".(b) S = {I, 2, 3, 4) and G = (Ci), (2 3)}.(c) S={I, 2, 3, 4, 5}andG={(I),(1 2),(1 3),(23),(123),(13 2)}.

ANSWER:

Step 1 of 4

Consider the relation  on permutation group G on S and define on S by

 If  for some.

Then is an equivalence relation on S.

Now, we need to find different equivalence classes in the following cases.

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