GATE 2021 MA – Question 55
F is a finite field whose nonzero multiplicative group contains a subgroup of order 17. Find the smallest possible |F|.
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Correct answer: 103 to 103
Explanation
A finite field has prime-power order q and cyclic nonzero group of order q−1. Thus 17 must divide q−1. The candidates 18,35,52,69,86 are not prime powers; the next, 103, is prime. The field 𝔽₁₀₃ exists and its multiplicative group of order 102 has an order-17 subgroup. Minimum **103**.