Let and be an odd prime such that for a prime factor of . We get a bound on the -rank of the class group of in terms of the -rank of the class group of a real quadratic subfield contained in . At the end we look into few numerical examples.
"Primary rank of the class group of real cyclotomic fields." Rocky Mountain J. Math. 50 (6) 2149 - 2155, December 2020. https://doi.org/10.1216/rmj.2020.50.2149