论文信息 - Algorithmic Methods for Finitely Generated Abelian Groups

Algorithmic Methods for Finitely Generated Abelian Groups

We describe algorithmic tools to compute with exact sequences of Abelian groups. Although simple in nature, these are essential for a number of applications such as the determination of the structure of (ZK/m)*for an ideal m of a number field K, of ray class groups of number fields, and of conductors of the corresponding Abelian extensions.

[1] Henri Cohen,et al. Computing Ray Class Groups, Conductors and Discriminants , 1996, ANTS.

[2] Henri Cohen,et al. Étude heuristique des groupes de classes des corps de nombres. , 1990 .

[3] Lynne M. Butler,et al. Subgroup Lattices and Symmetric Functions , 1994 .

[4] Helmut Hasse,et al. Number Theory , 2020, An Introduction to Probabilistic Number Theory.

[5] Garrett Birkhoff,et al. Subgroups of Abelian Groups , 1935 .

[6] Henri Cohen,et al. Class Groups of Number Fields: Numerical Heuristics , 1987 .

[7] Henri Cohen,et al. Advanced topics in computational number theory , 2000 .