COUNTEREXAMPLES TO A CONJECTURE OF LEMMERMEYER Nigel Boston and Charles Leedham-Green
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چکیده
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 Q, of quadratic number fields.
منابع مشابه
The F a , b , c conjecture is true , II
In 1977 a five-part conjecture was made about a family of groups related to trivalent graphs and subsequently two parts of the conjecture were proved. The conjecture completely determines all finite members of the family. Here we complete the proof of the conjecture by giving proofs for the remaining three parts. Dedicated to Charles Leedham-Green on the occasion of his 65th birthday
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تاریخ انتشار 2005