Sylow 2-subgroups of rational solvable groups Authors
First Online: 17 November 2011 Received: 06 May 2011 Accepted: 27 October 2011 DOI:
10.1007/s00209-011-0965-9 Cite this article as: Isaacs, I.M. & Navarro, G. Math. Z. (2012) 272: 937. doi:10.1007/s00209-011-0965-9
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.
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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