On certain quotients of $p$-class tower groups of quadratic fields

Michael R. Bush

On certain quotients of $p$-class tower groups of quadratic fields

Number Theory 2023-09-01 v2

Authors: Michael R. Bush

Abstract

A characterization of the quotients of $p$ -class tower groups of quadratic fields by terms in the lower $p$ -central series plays an important role in the formulation of conjectures by Boston, Hajir and the author about the distribution of such groups as the base field varies. In this paper, another equivalent criterion is given which resolves an issue that arose as part of the group-theoretical calculations carried out in relation to these conjectures.

Keywords

p-class tower groups quadratic fields lower p-central series group quotients equivalent criterion number theory conjectures

Cite

@article{arxiv.2001.01396,
  title  = {On certain quotients of $p$-class tower groups of quadratic fields},
  author = {Michael R. Bush},
  journal= {arXiv preprint arXiv:2001.01396},
  year   = {2023}
}

Comments

Made some minor structural changes and corrections. Added more details to the proof of Lemma 2.1

On certain quotients of $p$-class tower groups of quadratic fields

Abstract

Keywords

Cite

Comments

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