The cyclic structure of maximal tori of the finite classical groups
Algebra i logika, Tome 46 (2007) no. 2, pp. 129-156.

Voir la notice de l'article provenant de la source Math-Net.Ru

Maximal tori of all finite simple classical groups, as well as of special and general projective linear and unitary groups, are treated. For every such torus, its expression as a direct sum of cyclic groups is obtained in an explicit form.
Keywords: finite simple group, classical group, semisimple element, spectrum of a group.
Mots-clés : maximal torus
@article{AL_2007_46_2_a0,
     author = {A. A. Buturlakin and M. A. Grechkoseeva},
     title = {The cyclic structure of maximal tori of the finite classical groups},
     journal = {Algebra i logika},
     pages = {129--156},
     publisher = {mathdoc},
     volume = {46},
     number = {2},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2007_46_2_a0/}
}
TY  - JOUR
AU  - A. A. Buturlakin
AU  - M. A. Grechkoseeva
TI  - The cyclic structure of maximal tori of the finite classical groups
JO  - Algebra i logika
PY  - 2007
SP  - 129
EP  - 156
VL  - 46
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AL_2007_46_2_a0/
LA  - ru
ID  - AL_2007_46_2_a0
ER  - 
%0 Journal Article
%A A. A. Buturlakin
%A M. A. Grechkoseeva
%T The cyclic structure of maximal tori of the finite classical groups
%J Algebra i logika
%D 2007
%P 129-156
%V 46
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AL_2007_46_2_a0/
%G ru
%F AL_2007_46_2_a0
A. A. Buturlakin; M. A. Grechkoseeva. The cyclic structure of maximal tori of the finite classical groups. Algebra i logika, Tome 46 (2007) no. 2, pp. 129-156. http://geodesic.mathdoc.fr/item/AL_2007_46_2_a0/

[1] G. M. Seitz, “On the subgroup structure of classical groups”, Commun. Algebra, 10:8 (1982), 875–885 | DOI | MR | Zbl

[2] “R. W. Carter”, Proc. Lond. Math. Soc., III Ser., 42:1 (1981), 1–41 | DOI | MR

[3] Seminar po algebraicheskim gruppam, Mir, M., 1973 | MR

[4] R. W. Carter, Finite groups of Lie type. Conjugacy classes and complex characters, Pure Appl. Math., A Wiley-Interscience Publ., John Wiley and Sons, Chichester-New York etc., 1985 | MR | Zbl

[5] R. W. Carter, “Conjugacy classes in the Weyl group”, Compos. Math., 25:1 (1972), 1–59 | MR | Zbl

[6] R. W. Carter, Simple groups of Lie type, Pure Appl. Math., A Wiley-Interscience Publ., 28, John Wiley and Sons, London etc., 1972 | MR

[7] M. Aschbacher, Finite group theory, Cambridge Stud. Adv. Math., 10, Cambridge Univ. Press, Cambridge etc., 1986 | MR | Zbl

[8] P. Kleidman, M. Liebeck, The subgroup structure of the finite classical groups, London Math. Soc. Lect. Note Ser., 129, Cambridge Univ. Press, Cambridge etc., 1990 | MR | Zbl

[9] F. D. Veldkamp, “Regular elements in anisotropic tori”, Contributions to algebra., A collect. papers ded. E. Kolchin, eds. H. Bass, Ph. J. Cassidy, J. Kovacic, Academic Press, New York etc., 1977, 389–424 | MR