MATH 402A - Solutions for Homework Assignment 3
MATH 402A - Solutions for Homework Assignment 3 Problem 7, page 55: We wish to find C(a) for each a ∈ S3. It is clear that C(i) = S3. For any group G and any a ∈ G, it is clear that every power of a commutes with a and therefore (a) ⊆ C(a) . Assume that a ∈ S3 and a 6= i. Then a has order 2 or 3. Thus, the subgroup (a) of S3 has order ...
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