( G, *) is an abelian group. Then
2018
( G, *) is an abelian group. Then
- A.
x = x -1, for any x belonging to G
- B.
x = x2, for any x belonging to G
- C.
(x * y )2 = x2 * y2, for any x, y belonging to G
- D.
G is of finite order
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Correct answer: C
In an abelian group (G, *), the operation is commutative, meaning x * y = y * x for all x, y in G. Therefore, (x * y)^2 = (x * y) * (x * y) = x * (y * x) * y. By commutativity, y * x = x * y, so this becomes x * (x * y) * y = (x * x) * (y * y) = x^2 * y^2. This property holds for all elements in an abelian group.
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