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Nonabelian Fully-Ramified Sections

Published online by Cambridge University Press:  20 November 2018

Mark L. Lewis
Mark L. Lewis*
Affiliation:
Mathematics Department 400 Carver Hall Iowa State University Ames, Iowa 50011 U.S.A. email: mllewis@iastate.edu
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Abstract

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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.

Keywords

20C15
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 48 , Issue 5 , 01 October 1996 , pp. 997 - 1017
Copyright
Copyright © Canadian Mathematical Society 1996

References

1. DeMeyer, F. and Janusz, G., Finite Groups with an Irreducible Representation of Large Degree, Math, Z. 108(1969), 145–153.Google Scholar
2. Glauberman, G., Correspondences of Characters for Relatively Prime Operator Groups, Canad. J., Math. 20(1968), 1465–1488.Google Scholar
3. Huppert, B., Endlichen Gruppen I, Springer-Verlag, Berlin, 1967.Google Scholar
4. Isaacs, I.M., Characters of Solvable and Symplectic Groups, Amer. J., Math. 95(1973), 594–635.Google Scholar
5. Isaacs, I.M., Character Theory of Finite Groups, Academic Press, New York, 1976.Google Scholar
6. Isaacs, I.M., Characters of Solvable Groups, Proc. of Symp. in Pure, Math. 37(1980), 377–384.Google Scholar
7. Isaacs, I.M., Character Correspondences in Solvable Groups, Adv. in, Math. 43(1982), 284–306.Google Scholar
8. Isaacs, I.M. and Navarro, G., Character Correspondences and Irreducible Induction and Restriction, J., Algebra 140(1991), 131–140.Google Scholar
9. Lewis, M.L., Character Correspondences and Nilpotent Fully-Ramified Sections, Trans. Amer. Math. Soc, submitted.Google Scholar
10. Lewis, M.L., A New Canonical Character Correspondence in Solvable Groups, J. Algebra, submitted.Google Scholar
11. Lewis, M.L., The Canonical Correspondent and Constituents of Odd Multiplicity, preprint.Google Scholar
12. Lewis, M.L., A Family of Groups Containing a NonAbelian Fully-Ramified Section, J. Algebra, to appear.Google Scholar
13. Navarro, G., Fong Characters and Correspondences in π -Separable Groups, Canad. J., Math. 43(1991), 405–412.Google Scholar
14. Navarro, G., Correspondences and Irreducible Products of Characters, J., Algebra 158(1993), 492–498.Google Scholar
15. Navarro, G., Some Open Problems on Coprime Action and Character Correspondences, Bull. London Math., Soc. 26(1994), 513–522.Google Scholar
16. Wolf, T.R., Character Correspondences in Solvable Groups, Illnois J., Math. 22(1978), 327–340.Google Scholar
17. Wolf, T.R., Character Correspondences Induced by Subgroups of Operator Groups, J., Algebra 57(1979), 502–521.Google Scholar
18. Wolf, T.R., Character Correspondences and π-Special Characters in π -Separable Groups, Canad. J., Math. 39(1987), 920–937.Google Scholar