Archiv der Mathematik

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

Counterexamples to a conjecture of Lemmermeyer

  • Nigel Boston
  • 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 Q, of quadratic number fields.


Galois Group Number Field Quadratic Number Quadratic Number Field 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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

Personalised recommendations