 Solution

ID: past-exam-of-the-algebra-course-of-the-university-of-oxford/2011/6/a/i/solution

2

has order eight. Every one of its nonidentity elements lies in the only even-order class, so has order two. In a group of exponent two,

x y = (x y)^{- 1} = y^{- 1} x^{- 1} = y x .

S ≅ C_{2}^{3}

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