Hostname: page-component-77c89778f8-gq7q9 Total loading time: 0 Render date: 2024-07-22T18:21:58.227Z Has data issue: false hasContentIssue false
  • English
  • Français

Coprime actions and degrees of primitive inducers of invariant characters

Published online by Cambridge University Press:  17 April 2009

Alexander Moretó  and
Lucía Sanus
Alexander Moretó
Affiliation:
Departamento de Matemáticas, Facultad de Ciencias, Universidad del País Vasco, 48080 Bilbao, Spain, e-mail: mtbmoqua@lg.ehu.es
Lucía Sanus
Affiliation:
Departament d'Àlgebra, Universitat de València, 46100 Burjassot, València, Spain, e-mail: lucia.sanus@uv.es
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let a finite group A act coprimely on a finite group G and χ ∈ Irr A(G). Isaacs, Lewis and Navarro proved that if G is nilpotent then the degrees of any two A-primitive characters of A-invariant subgroups of G inducing χ coincide. In this note we aim at extending this result by weakening the hypothesis on G.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 64 , Issue 2 , October 2001 , pp. 315 - 320
Copyright
Copyright © Australian Mathematical Society 2001

References

[1]Dade, E.C., ‘Monomial characters and normal subgroups’, Math. Z. 178 (1981), 401–420.CrossRefGoogle Scholar
[2]Isaacs, I.M., ‘Characters of π-separable groups’, J. Algebra 86 (1984), 98–128.CrossRefGoogle Scholar
[3]Isaacs, I.M., Character theory of finite groups (New york, Dover, 1994).Google Scholar
[4]Isaacs, I.M., Lewis, M.L. and Navarro, G., ‘Invariant characters and coprime action on finite nilpotent groups’, Arch. Math. 74 (2000), 401–409.CrossRefGoogle Scholar
[5]Isaacs, I.M. and Navarro, G., ‘Character correspondences and irreducible induction and restriction’, J. Algebra 140 (1991), 131–140.CrossRefGoogle Scholar
[6]Lewis, M.L., ‘Inducing characters of prime power degree’, Osaka J. Math. 37 (2000), 735–744.Google Scholar
[7]Manz, O., Wolf, T.R., Representations of solvable groups, London Math. Society Lecture Notes Series 185 (Cambridge University Press, Cambridge, 1993).CrossRefGoogle Scholar