# Masaryk University

Publication details

# Class Number Parity of a Compositum of Five Quadratic Fields

Authors 2002 Article in Periodical Acta Math. et Informatica Univ. Ostraviensis General mathematics class number; cyclotomic unit; crossed homomorphism In this paper we show that the class number of the field $Q(\sqrt p,\sqrt q,\sqrt r,\sqrt s,\sqrt t)$ is even for $p,q,r,s,t$ being different primes either equal to 2 or congruent to 1 modulo 4. This result is based on our previous results about the parity of the class number in the case of the field $Q{\sqrt p,\sqrt q,\sqrt r}$.