# 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} }

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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