Note on class number parity of an abelian field of prime conductor, II

For a fixed integer n >= 1, let p = 2nl + 1 be a prime number with an odd prime number l, and let F = F-p,( l )be the real abelian field of conductor p and degree l. We show that the class number h(F) of F is odd when 2 remains prime in the real lth cyclotomic field Q(zeta(l))(+) and l is sufficiently large.