English

Counterexamples to a conjecture of Lemmermeyer

Number Theory 2007-05-23 v1

Abstract

We produce infinitely many finite 2-groups that do not embed with index 2 in any group generated by involutions. This disproves a conjecture of Lemmermeyer and restricts the possible Galois groups of unramified 2-extensions, Galois over the rationals, of quadratic number fields.

Keywords

Cite

@article{arxiv.math/9808146,
  title  = {Counterexamples to a conjecture of Lemmermeyer},
  author = {Nigel Boston and Charles Leedham-Green},
  journal= {arXiv preprint arXiv:math/9808146},
  year   = {2007}
}
R2 v1 2026-07-22T17:59:47.879Z