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}
}