Mathematische Zeitschrift

, Volume 272, Issue 3–4, pp 937–945

Sylow 2-subgroups of rational solvable groups



A long-standing conjecture proposes that a Sylow 2-subgroup S of a finite rational group must be rational. In this paper we provide a counterexample to this conjecture, but we show that if G is solvable and S has nilpotence class 2, then S actually is rational.


Rational group Sylow 2-subgroup 2-rational 

Mathematics Subject Classification (2010)

20C15 20D10 20D20 


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of WisconsinMadisonUSA
  2. 2.Departament d’AlgebraUniversitat de ValenciaBurjassot, ValenciaSpain

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