Sylow 2-subgroups of rational solvable groups
First Online: 17 November 2011 Received: 06 May 2011 Accepted: 27 October 2011 DOI:
Cite this article as: Isaacs, I.M. & Navarro, G. Math. Z. (2012) 272: 937. doi:10.1007/s00209-011-0965-9 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
Most of this paper was written while the second author was visiting at the University of Wisconsin, Madison. His research was partially supported by the Spanish Ministerio de Educación y Ciencia, proyecto MTM2010-15296, Programa de Movilidad, and Prometeo/Generalitat Valenciana.
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