Question

Q: The order of center of a dihedral group having an even degree is​

Answer 1

Answer:

The center of the dihedral Galois group. If n is even, the center of Dn has order 2. For determining the center, we use any odd prime p ∈ such that f mod p is irreducible; the proportion of such primes in the dihedral case, according to Proposition 2.2, is φ(n)/2n. Proposition 3.1.