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