Counterexamples to a conjecture of Lemmermeyer, by Nigel Boston and Charles Leedham-Green

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.

Nigel Boston and Charles Leedham-Green <boston@math.uiuc.edu, C.R.Leedham-Green@qmw.ac.uk>