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Archiv der Mathematik

, Volume 72, Issue 3, pp 177–179 | Cite as

Counterexamples to a conjecture of Lemmermeyer

  • Nigel Boston
  • Charles Leedham-Green
Article

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 Q, of quadratic number fields.

Keywords

Galois Group Number Field Quadratic Number Quadratic Number Field 

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Copyright information

© Birkhäuser Verlag, Basel 1999

Authors and Affiliations

  • Nigel Boston
    • 1
  • Charles Leedham-Green
    • 2
  1. 1.Department of Mathematics, University of Illinois, Urbana, Illinois 61801, USAUS
  2. 2.School of Mathematical Sciences, Queen Mary and Westfield College, University of London, Mile End Road, London E1 4NS, EnglandEngland

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