Geodesic
Nonabelian Fully-Ramified Sections
Canadian journal of mathematics, Tome 48 (1996) no. 5, pp. 997-1017

Voir la notice de l'article provenant de la source Cambridge University Press

Let G be a finite group and let K and L be normal subgroups of G such that |K : L| and |G : K| are relatively prime, and assume that |K : L| is odd. Let H be a subgroup of G such that G = HK and H ∩ K = L. Let φ be an irreducible character of L that is invariant under the action of L and is fully ramified with respect to K/L. If χ ∈ Irr(G) is a constituent of φG, then we prove that χH has a unique irreducible constituent having odd multiplicity.
DOI : 10.4153/CJM-1996-052-8
Mots-clés : 20C15 
Lewis, Mark L. Nonabelian Fully-Ramified Sections. Canadian journal of mathematics, Tome 48 (1996) no. 5, pp. 997-1017. doi: 10.4153/CJM-1996-052-8
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[1] 1. DeMeyer, F. and Janusz, G., Finite Groups with an Irreducible Representation of Large Degree, Math, Z. 108(1969), 145–153. Google Scholar

[2] 2. Glauberman, G., Correspondences of Characters for Relatively Prime Operator Groups, Canad. J., Math. 20(1968), 1465–1488. Google Scholar

[3] 3. Huppert, B., Endlichen Gruppen I, Springer-Verlag, Berlin, 1967. Google Scholar

[4] 4. Isaacs, I.M., Characters of Solvable and Symplectic Groups, Amer. J., Math. 95(1973), 594–635. Google Scholar

[5] 5. Isaacs, I.M., Character Theory of Finite Groups, Academic Press, New York, 1976. Google Scholar

[6] 6. Isaacs, I.M., Characters of Solvable Groups, Proc. of Symp. in Pure, Math. 37(1980), 377–384. Google Scholar

[7] 7. Isaacs, I.M., Character Correspondences in Solvable Groups, Adv. in, Math. 43(1982), 284–306. Google Scholar

[8] 8. Isaacs, I.M. and Navarro, G., Character Correspondences and Irreducible Induction and Restriction, J., Algebra 140(1991), 131–140. Google Scholar

[9] 9. Lewis, M.L., Character Correspondences and Nilpotent Fully-Ramified Sections, Trans. Amer. Math. Soc, submitted. Google Scholar

[10] 10. Lewis, M.L., A New Canonical Character Correspondence in Solvable Groups, J. Algebra, submitted. Google Scholar

[11] 11. Lewis, M.L., The Canonical Correspondent and Constituents of Odd Multiplicity, preprint. Google Scholar

[12] 12. Lewis, M.L., A Family of Groups Containing a NonAbelian Fully-Ramified Section, J. Algebra, to appear. Google Scholar

[13] 13. Navarro, G., Fong Characters and Correspondences in π -Separable Groups, Canad. J., Math. 43(1991), 405–412. Google Scholar

[14] 14. Navarro, G., Correspondences and Irreducible Products of Characters, J., Algebra 158(1993), 492–498. Google Scholar

[15] 15. Navarro, G., Some Open Problems on Coprime Action and Character Correspondences, Bull. London Math., Soc. 26(1994), 513–522. Google Scholar

[16] 16. Wolf, T.R., Character Correspondences in Solvable Groups, Illnois J., Math. 22(1978), 327–340. Google Scholar

[17] 17. Wolf, T.R., Character Correspondences Induced by Subgroups of Operator Groups, J., Algebra 57(1979), 502–521. Google Scholar

[18] 18. Wolf, T.R., Character Correspondences and π-Special Characters in π -Separable Groups, Canad. J., Math. 39(1987), 920–937. Google Scholar

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