Geodesic
Fong Characters and Correspondences in π-Separable Groups
Canadian journal of mathematics, Tome 43 (1991) no. 2, pp. 405-412

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

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.
DOI : 10.4153/CJM-1991-023-9
Mots-clés : 20C15 
Navarro, Gabriel. Fong Characters and Correspondences in π-Separable Groups. Canadian journal of mathematics, Tome 43 (1991) no. 2, pp. 405-412. doi: 10.4153/CJM-1991-023-9
@article{10_4153_CJM_1991_023_9,
     author = {Navarro, Gabriel},
     title = {Fong {Characters} and {Correspondences} in {\ensuremath{\pi}-Separable} {Groups}},
     journal = {Canadian journal of mathematics},
     pages = {405--412},
     year = {1991},
     volume = {43},
     number = {2},
     doi = {10.4153/CJM-1991-023-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1991-023-9/}
}
TY  - JOUR
AU  - Navarro, Gabriel
TI  - Fong Characters and Correspondences in π-Separable Groups
JO  - Canadian journal of mathematics
PY  - 1991
SP  - 405
EP  - 412
VL  - 43
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1991-023-9/
DO  - 10.4153/CJM-1991-023-9
ID  - 10_4153_CJM_1991_023_9
ER  - 
%0 Journal Article
%A Navarro, Gabriel
%T Fong Characters and Correspondences in π-Separable Groups
%J Canadian journal of mathematics
%D 1991
%P 405-412
%V 43
%N 2
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1991-023-9/
%R 10.4153/CJM-1991-023-9
%F 10_4153_CJM_1991_023_9

[1] 1. Glauberman, G., Correspondence of characters for relatively prime operator groups, Can. J. Math. 20(1968), 1465-1488. Google Scholar

[2] 2. Huppert, B., Endliche Grupen I. Springer-Verlag, Berlin - Heildelberg - New York - Tokyo, 1983. Google Scholar

[3] 3. Isaacs, I.M., Characters of solvable and symplectic groups, Amer. J. Math. 95(1973), 594–635. Google Scholar

[4] 4. Isaacs, I.M., Character theory of finite groups. Academic Press, New York, 1976. Google Scholar

[5] 5. Isaacs, I.M., Character of π-separable groups, J. Algebra 86(1984), 98–128. Google Scholar

[6] 6. Isaacs, I.M., Fong characters in π-separable groups, J. Algebra 99(1986), 89–107. Google Scholar

[7] 7. Isaacs, I.M., G. Navarro, Character correspondences and irreducible induction and restriciton, to appear in J. Algebra. Google Scholar

[8] 8. Uno, K., Character correspondences in p-solvable groups, Osaka J. Math. 20(1983), 713–725. Google Scholar

[9] 9. Willems, W., On the projectives of a group algebra, Math. Z. 171(1980), 163–174. Google Scholar

[10] 10. Wolf, T.R., Character correspondence in solvable groups, Illinois J. Math. 22(1978), 327–340. Google Scholar

[11] 11. Wolf, T.R., Character correspondences induced by subgroups of operator groups, J. Algebra 57(1979), 502- 521. Google Scholar

[12] 12. Wolf, T.R., Character correspondences and π-special characters in -π-separable groups, Can. J. Math. (4) 39(1987), 920–937. Google Scholar

Cité par Sources :