# Subgroups of Class Groups of Algebraic Quadratic Function Fields

## Related Articles

- Weighted Distribution of the 4-rank of Class Groups and Applications. Fouvry, Étienne; Klüners, Jürgen // IMRN: International Mathematics Research Notices;Aug2011, Vol. 2011 Issue 16, p3618
We prove that the distribution of the values of the 4-rank of ideal class groups of quadratic fields is not affected when it is weighted by a divisor type function. We then give several applications concerning a new lower bound of the sums of class numbers of real quadratic fields with...

- Some Results Connected with the Class Number Problem in Real Quadratic Fields. Grytczuk, Aleksander; Grytczuk, Jarosław // Acta Mathematica Sinica;Oct2005, Vol. 21 Issue 5, p1107
We investigate arithmetic properties of certain subsets of square-free positive integers and obtain in this way some results concerning the class number h( d) of the real quadratic field $$ \mathbb{Q}{\left( {{\sqrt d }} \right)} $$. In particular, we give a new proof of the result of Hasse,...

- CONSTRUCTION OF CLASS FIELDS OVER IMAGINARY QUADRATIC FIELDS AND APPLICATIONS. BUMKYU CHO; JA KYUNG KOO // Quarterly Journal of Mathematics;Jun2010, Vol. 61 Issue 2, p199
Let K be an imaginary quadratic field, Hî”® the ring class field of an order î”® in K and K(N) be the ray class field modulo N over K for a positive integer N. In this paper we provide certain general techniques of finding Hî”® and K(N) by using the theory of Shimura's canonical...

- COHOMOLOGICAL INVARIANTS OF MAPPING CLASS GROUPS. PRIDDY, STEWART; XIA, YINING // Quarterly Journal of Mathematics;1996, Vol. 47 Issue 3, p361
The article discusses a series of cohomological integral invariants of mapping class groups, which is defined as the group of path components of orientation preserving diffeomorphisms of an oriented closed surface. It states that the calculation of integral invariants can be done by using some...

- Groups with Almost Normal Subgroups of Infinite Rank. Semko, N.; Kuchmenko, S. // Ukrainian Mathematical Journal;Apr2005, Vol. 57 Issue 4, p621
We study classes of groups whose subgroups of some infinite ranks are almost normal.

- The cardinal coefficients of the Ideal $${{\mathcal {I}}_{f}}$$. Osuga, Noboru; Kamo, Shizuo // Archive for Mathematical Logic;Nov2008, Vol. 47 Issue 7/8, p653
In 2002, Yorioka introduced the s-ideal $${{\mathcal {I}}_f}$$ for strictly increasing functions f from ? into ? to analyze the cofinality of the strong measure zero ideal. For each f, we study the cardinal coefficients (the additivity, covering number, uniformity and cofinality) of $${{\mathcal...

- Differents, discriminants and Steinitz classes. Schmid, Peter // Bulletin of the London Mathematical Society;Apr2013, Vol. 45 Issue 2, p318
Let L|K be an extension of algebraic number fields. By a theorem of Hecke, the ideal class of the different î•£L|K is a square in ClL. Whereas the class of the discriminant î–ƒL|K=NL|K(î•£L|K) is the square of the Steinitz class sL|K in ClK, which vanishes if and only if the ring RL...

- The Rabinowitsch-Mollin-Williams Theorem Revisited. Mollin, R. A. // International Journal of Mathematics & Mathematical Sciences;2009, p1
We completely classify all polynomials of type (x2 + x -(Î”-1))/4 which are prime or 1 for a range of consecutive integers x â‰¥ 0, called Rabinowitsch polynomials, where Î” â‰¡ 1(mod4) with Î” > 1 square-free. This corrects, extends, and completes the results by Byeon and Stark...

- A characterization of the family of external lines to a quadratic cone of PG(3, q), q. Di Gennaro, R.; Durante, N.; Olanda, D. // Journal of Geometry;2010, Vol. 96 Issue 1/2, p63
In this paper we characterize the family of external lines to a quadratic cone of PG(3, q), q odd, by their intersection properties with points and planes of the space.