Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-27T02:21:52.842Z Has data issue: false hasContentIssue false
  • English
  • Français

Fong Characters and Correspondences in π-Separable Groups

Published online by Cambridge University Press:  20 November 2018

Gabriel Navarro
Gabriel Navarro*
Affiliation:
Departamento de Algebra Facultad de Matemáticas Universitat de Valencia BurjassotValencia Spain
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 G and S be finite groups. Suppose that S acts on G with (|G|, |S| ) = 1. If S is solvable, Glauberman showed the existence of a natural bijection from lrrs(G) = ﹛ χ ∈ Irr(G) | χs = χ for a11 s ∈ S﹜ on to Irr(C), where C = CG(S). If S is not solvable, and consequently | G| is odd, Isaacs also proved the existence of a natural bijection between the above set of characters. Finally, Wolf proved that both maps agreed when both were defined ([1], [3], [10]). As in [7], let us denote by *: Irrs(G) → Irr(C) the Glauberman-Isaacs Correspondence.

Keywords

20C15
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 43 , Issue 2 , 01 April 1991 , pp. 405 - 412
Copyright
Copyright © Canadian Mathematical Society 1991

References

1. Glauberman, G., Correspondence of characters for relatively prime operator groups, Can. J. Math. 20(1968), 1465-1488.Google Scholar
2. Huppert, B., Endliche Grupen I. Springer-Verlag, Berlin - Heildelberg - New York - Tokyo, 1983.Google Scholar
3. Isaacs, I.M., Characters of solvable and symplectic groups, Amer. J. Math. 95(1973), 594–635.Google Scholar
4. Isaacs, I.M., Character theory of finite groups. Academic Press, New York, 1976.Google Scholar
5. Isaacs, I.M., Character of π-separable groups, J. Algebra 86(1984), 98–128.Google Scholar
6. Isaacs, I.M., Fong characters in π-separable groups, J. Algebra 99(1986), 89–107.Google Scholar
7. Isaacs, I.M., G. Navarro, Character correspondences and irreducible induction and restriciton, to appear in J. Algebra.Google Scholar
8. Uno, K., Character correspondences in p-solvable groups, Osaka J. Math. 20(1983), 713–725.Google Scholar
9. Willems, W., On the projectives of a group algebra, Math. Z. 171(1980), 163–174.Google Scholar
10. Wolf, T.R., Character correspondence in solvable groups, Illinois J. Math. 22(1978), 327–340.Google Scholar
11. Wolf, T.R., Character correspondences induced by subgroups of operator groups, J. Algebra 57(1979), 502- 521.Google Scholar
12. Wolf, T.R., Character correspondences and π-special characters in -π-separable groups, Can. J. Math. (4) 39(1987), 920–937.Google Scholar