Sylow 2-subgroups of rational solvable groups Authors
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.
Download to read the full article text References
Gluck, D.: Rational defect groups and 2-rational characters. J. Group Theory (Published on-line Jan. 12, 2011)
Isaacs I.M.: Characters of solvable and symplectic groups. Am. J. Math.
, 594–635 (1973)
MathSciNet MATH CrossRef
Isaacs, I.M.: Character theory of finite groups. AMS Chelsea, Providence (2006) (Corrected reprint of 1976 original)
Isaacs, I.M., Karagueuzian, D.: Conjugacy in groups of upper triangular matrices. J. Algebr. 202, 704–711 (1998) [Erratum, J. Algebr. 208, 722 (1998)]
Kletzing, D.: Structure and representations of Q-groups. Lecture Notes in Mathematics, vol. 1084. Springer, Berlin (1984)