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3. a) For any group G and any a∈G, prove that given any k∈Z+, C(a) ⊆...

3. a) For any group G and any a∈G, prove that given any k∈Z+, C(a) ⊆ C(ak).

(HINT: You are being asked to show that C(a) is a subset of C(ak). You can prove this by proving that if x ∈ C(a), then x must also be an element of C(ak) for any positive integer k.)

b) Is it necessarily true that C(a) = C(ak) for any k ∈ Z+? Either prove or disprove this claim.

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