Relative class numbers inside the \(p\)th cyclotomic field (Q2215994)

Any prime number \(p\equiv 3\pmod{4}\) can be written (not uniquely) in the form \(p=2nl^f+1\) for some odd \(n\) and prime \(l\) with \(l\nmid n\). Now, for every \(0\leq t\leq f\) we can define \(K_t\) the imaginary subfield of \(\mathbb{Q}(\zeta_p)\) of degree \(t\) and let \(h_t^{-}\) the relative class number of \(K_t\). In this paper, the authors give some divisibility results about the the ratio \(h_t^{-}/h_{t-1}^{-}\).