Annihilator ideals of two-generated metabelian p-groups

DOI10.1142/S0219498818500767zbMath1441.20011arXiv1603.09288OpenAlexW2962742444MaRDI QIDQ4638611

Daniel C. Mayer

Publication date: 27 April 2018

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1603.09288

zbMATH Keywords

commutator calculusresidue class ringscentral seriesaction on the commutator subgroupideals of bivariate polynomials with integer coefficientsmetabelian \(p\)-groups with two generatorssecond Hilbert \(p\)-class fields

Mathematics Subject Classification ID

Generators, relations, and presentations of groups (20F05) Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Class field theory (11R37) Finite nilpotent groups, (p)-groups (20D15) Derived series, central series, and generalizations for groups (20F14) Commutator calculus (20F12)

Uses Software

• SmallGroups Library

Cites Work

• The distribution of second \(p\)-class groups on coclass graphs
• Transfers of metabelian \(p\)-groups
• 3-class field towers of exact length 3
• On a special class of \(p\)-groups
• Groups of prime power order. Vol. 1.
• Class field towers of imaginary quadratic fields
• Principalization algorithm via class group structure
• The Groups of Order p 6 (p and Odd Prime)
• The Metabelian p-Groups of Maximal Class
• A MILLENNIUM PROJECT: CONSTRUCTING SMALL GROUPS
• On Gauss's Class Number Problems
• Metabelian p-Groups of Maximal Class
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