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.
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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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Isaacs, I.M., Navarro, G. Sylow 2-subgroups of rational solvable groups. Math. Z. 272, 937–945 (2012). https://doi.org/10.1007/s00209-011-0965-9
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DOI: https://doi.org/10.1007/s00209-011-0965-9