Class Number Parity of a Compositum of Five Quadratic Fields

BULANT, Michal. Class Number Parity of a Compositum of Five Quadratic Fields. Acta Math. et Informatica Univ. Ostraviensis. Ostrava (CZ), 2002, vol. 2002, No 10, p. 25-34. ISSN 1211-4774.

Basic information

• Original name: Class Number Parity of a Compositum of Five Quadratic Fields
• Authors: BULANT, Michal (203 Czech Republic, guarantor).
• Edition: Acta Math. et Informatica Univ. Ostraviensis, Ostrava (CZ), 2002, 1211-4774.

Other information

• Original language: English
• Type of outcome: Article in a journal
• Field of Study: 10101 Pure mathematics
• Country of publisher: Czech Republic
• Confidentiality degree: is not subject to a state or trade secret
• RIV identification code: RIV/00216224:14310/02:00006776
• Organization unit: Faculty of Science
• Keywords in English: class number; cyclotomic unit; crossed homomorphism
• Tags: class number, crossed homomorphism, cyclotomic unit

Abstract

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 $Q{\sqrt p,\sqrt q,\sqrt r}$.

Links

• GA201/01/0471, research and development project: Name: Algebraické, analytické a kombinatorické metody teorie čísel

Investor: Czech Science Foundation, Algebraic, analytic and combinatorial methods of number theory