Sylow 2-subgroups of rational solvable groups
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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.
KeywordsRational group Sylow 2-subgroup 2-rational
Mathematics Subject Classification (2010)20C15 20D10 20D20
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- 1.Gluck, D.: Rational defect groups and 2-rational characters. J. Group Theory (Published on-line Jan. 12, 2011)Google Scholar
- 3.Isaacs, I.M.: Character theory of finite groups. AMS Chelsea, Providence (2006) (Corrected reprint of 1976 original)Google Scholar
- 4.Isaacs, I.M., Karagueuzian, D.: Conjugacy in groups of upper triangular matrices. J. Algebr. 202, 704–711 (1998) [Erratum, J. Algebr. 208, 722 (1998)]Google Scholar
- 5.Kletzing, D.: Structure and representations of Q-groups. Lecture Notes in Mathematics, vol. 1084. Springer, Berlin (1984)Google Scholar