Ambiguous Numbers over $P(\zeta_3)$ of Absolutely Abelian Extensions of Degree 6

Class numbers of some abelian extensions of rational function fields

Let P be a monic irreducible polynomial. In this paper we generalize the determinant formula for h(K Pn) of Bae and Kang and the formula for h−(KPn ) of Jung and Ahn to any subfields K of the cyclotomic function field KPn . By using these formulas, we calculate the class numbers h −(K), h(K+) of all subfields K of KP when q and deg(P ) are small.

Absolutely Abnormal Numbers

On component extensions locally compact abelian groups

Let $pounds$ be the category of locally compact abelian groups and $A,Cin pounds$. In this paper, we define component extensions of $A$ by $C$ and show that the set of all component extensions of $A$ by $C$ forms a subgroup of $Ext(C,A)$ whenever $A$ is a connected group. We establish conditions under which the component extensions split and determine LCA groups which are component projective. ...

On Galois Groups of Abelian Extensions over Maximal Cyclotomic Fields

Let k0 be a finite algebraic number field in a fixed algebraic closure Ω and ζn denote a primitive n-th root of unity ( n ≥ 1). Let k∞ be the maximal cyclotomic extension of k0, i.e. the field obtained by adjoining to k0 all ζn ( n = 1, 2, ...). Let M and L be the maximal abelian extension of k∞ and the maximal unramified abelian extension of k∞ respectively. The Galois groups Gal(M/k∞) and Gal...

Some Properties of Extensions of Small Degree over Q

This paper demonstrates a few characteristics of finite extensions of small degree over the rational numbers Q. It comprises attempts at classification of all such extensions of degrees 2, 3, and 4, as well as mention of how one might begin the process of classifying all finite fields with degree a power of 2. Some topics discussed are discriminants of certain fields, how to represent a given e...