Article

Mathematische Zeitschrift

, Volume 272, Issue 3, pp 937-945

First online:

Sylow 2-subgroups of rational solvable groups

  • I. M. IsaacsAffiliated withDepartment of Mathematics, University of Wisconsin Email author 
  • , Gabriel NavarroAffiliated withDepartament d’Algebra, Universitat de Valencia

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Abstract

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.

Keywords

Rational group Sylow 2-subgroup 2-rational

Mathematics Subject Classification (2010)

20C15 20D10 20D20