Department of Mathematics, K.T.H.M. College, Nashik

mathsbeauty

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Registered: 11-06-2015

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Number of Subfields (Part B Question: NET June-2015)

(Part B Question: NET June-2015) The number of subfields of a field \(F \) of cardinality \(2^{100} \) is
A. 2
B. 4
C. 9
D. 100

\(\textbf{Option C}\)
No. of subfields of \(F \) = no. of divisors of \(100 (= 2^2 \times 5^2) = (2 +1) \times (2+1) = 9\)