Genus group of finite Galois extensions

Author:
Teruo Takeuchi

Journal:
Proc. Amer. Math. Soc. **98** (1986), 211-214

MSC:
Primary 11R37

DOI:
https://doi.org/10.1090/S0002-9939-1986-0854020-6

MathSciNet review:
854020

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let be a Galois extension of finite degree, and let denote the maximal abelian extension over contained in the Hilbert class field of . We give formulas about the group structure of and the genus group of , which refine the ordinary genus formula.

**[1]**Yoshiomi Furuta,*The genus field and genus number in algebraic number fields*, Nagoya Math. J.**29**(1967), 281–285. MR**0209260****[2]**Tomio Kubota,*Galois group of the maximal abelian extension over an algebraic number field*, Nagoya Math. J.**12**(1957), 177–189. MR**0098077****[3]**Hiroo Miki,*On the maximal Abelian 𝑙-extension of a finite algebraic number field with given ramification*, Nagoya Math. J.**70**(1978), 183–202. MR**0480420****[4]**I. R. Šfarevič,*Extensions with given points of ramification*, Inst. Hautes Études Sci. Publ. Math.**18**(1963), 71-95; Amer. Math. Soc. Transl.**59**(1966), 128-149.

Retrieve articles in *Proceedings of the American Mathematical Society*
with MSC:
11R37

Retrieve articles in all journals with MSC: 11R37

Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1986-0854020-6

Article copyright:
© Copyright 1986
American Mathematical Society