Criteria for Three-Stage Towers of p-Class Fields

@article{Mayer2016CriteriaFT,
  title={Criteria for Three-Stage Towers of p-Class Fields},
  author={Daniel C. Mayer},
  journal={Advances in Pure Mathematics},
  year={2016},
  volume={07},
  pages={135-179}
}
  • Daniel C. Mayer
  • Published 2016
  • Mathematics
  • Advances in Pure Mathematics
  • Let p be a prime and K be a number field with non-trivial p-class group ClpK. A crucial step in identifying the Galois group G∞p of the maximal unramified pro-p extension of K is to determine its two-stage approximation M=G2pk, that is the second derived quotient MsG/Gn. The family τ1K of abelian type invariants of the p-class groups ClpL of all unramified cyclic extensions L/K of degree p is called the index- abelianization data (IPAD) of K. It is able to specify a finite batch of contestants… CONTINUE READING

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    Publications referenced by this paper.
    SHOWING 1-10 OF 48 REFERENCES
    THE SECOND p-CLASS GROUP OF A NUMBER FIELD
    • 30
    • PDF
    Recent progress in determining p-class field towers
    • 10
    • PDF
    Heuristics for p-class towers of imaginary quadratic fields
    • 29
    • Highly Influential
    • PDF
    The distribution of second p-class groups on coclass graphs
    • 23
    • PDF
    Transfers of metabelian p-groups
    • 28
    • PDF
    p-Capitulation over number fields with p-class rank two
    • 7
    • PDF
    Periodic sequences of p-class tower groups
    • 13
    • PDF
    New number fields with known p-class tower
    • 9
    • PDF
    On 3-groups of second maximal class
    • 24
    • Highly Influential
    • PDF
    Maximal unramified 3-extensions of imaginary quadratic fields and SL2(Z3)
    • 14
    • Highly Influential
    • PDF