Products of conjugacy classes in finite unitary groups GU(3,q 2 ) and SU(3,q 2 )
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 22 (2013) no. 2, pp. 219-251.

Pour les groupes GU(3), SU(3), GL(3), SU(3) sur un corps fini on résout le problème du produit des classes, c-à-d, on donne une liste complète de tous les m-uplets de classes de conjugaison dont le produit ne contient pas la matrice identité.

For the groups GU(3), SU(3), GL(3), SU(3) over a finite field we solve the class product problem, i.e., we give a complete list of m-tuples of conjugacy classes whose product does not contain the identity matrix.

DOI : 10.5802/afst.1371
Orevkov, S.Yu. 1

1 Institut des Mathématiques de Toulouse, UPS, 118 route de Narbonne, 31062 Toulouse, France
@article{AFST_2013_6_22_2_219_0,
     author = {Orevkov, S.Yu.},
     title = {Products of conjugacy classes in finite unitary groups $GU(3,q^2)$ and $SU(3,q^2)$},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {219--251},
     publisher = {Universit\'e Paul Sabatier, Institut de math\'ematiques},
     address = {Toulouse},
     volume = {Ser. 6, 22},
     number = {2},
     year = {2013},
     doi = {10.5802/afst.1371},
     zbl = {1283.20059},
     language = {en},
     url = {http://archive.numdam.org/articles/10.5802/afst.1371/}
}
TY  - JOUR
AU  - Orevkov, S.Yu.
TI  - Products of conjugacy classes in finite unitary groups $GU(3,q^2)$ and $SU(3,q^2)$
JO  - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY  - 2013
SP  - 219
EP  - 251
VL  - 22
IS  - 2
PB  - Université Paul Sabatier, Institut de mathématiques
PP  - Toulouse
UR  - http://archive.numdam.org/articles/10.5802/afst.1371/
DO  - 10.5802/afst.1371
LA  - en
ID  - AFST_2013_6_22_2_219_0
ER  - 
%0 Journal Article
%A Orevkov, S.Yu.
%T Products of conjugacy classes in finite unitary groups $GU(3,q^2)$ and $SU(3,q^2)$
%J Annales de la Faculté des sciences de Toulouse : Mathématiques
%D 2013
%P 219-251
%V 22
%N 2
%I Université Paul Sabatier, Institut de mathématiques
%C Toulouse
%U http://archive.numdam.org/articles/10.5802/afst.1371/
%R 10.5802/afst.1371
%G en
%F AFST_2013_6_22_2_219_0
Orevkov, S.Yu. Products of conjugacy classes in finite unitary groups $GU(3,q^2)$ and $SU(3,q^2)$. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 22 (2013) no. 2, pp. 219-251. doi : 10.5802/afst.1371. http://archive.numdam.org/articles/10.5802/afst.1371/

[1] Arad (Z.), Herzog (M.) (eds.).— Products of conjugacy classes in groups Lecture Notes in Math. 1112, Springer-Verlag, Berlin, Heidelberg, N.Y., Tokyo (1985). | MR | Zbl

[2] Agnihotri (S.), Woodward (C.).— Eigenvalues of products of unitary matrices and quantum Schubert calculus, Math. Research Letters, 5, p. 817-836 (1998). | MR | Zbl

[3] Belkale (P.).— Local systems on 1 -S for S a finite set, Compos. Math., 129, p. 67-86 (2001). | MR | Zbl

[4] Dickson (L. E.).— Linear groups with an exposition of the Galois field theory, Teubner, addr Leipzig (1901).

[5] Ennola (V.).— On the conjugacy classes of the finite unitary groups, Ann. Acad. Sci. Fennicae, Ser. A I., 313, p. 3-13 (1962). | MR | Zbl

[6] Ennola (V.).— On the characters of the finite unitary groups, Ann. Acad. Sci. Fennicae, Ser. A I., 323, p. 3-35 (1963). | MR | Zbl

[7] GAP software; the file ctgeneri.tbl.

[8] Geck (M.).— Diploma thesis.

[9] Gordeev (N. L.).— Products of conjugacy classes in perfect linear groups. Extended covering number, Zapiski Nauchn. Semin. POMI, 321 (2005), p. 67-89, Russian, English transl., J. Math. Sci., 136, p. 3867-3879 (2006). | MR | Zbl

[10] Karni (S.).— Covering number of groups of small order and sporadic groups, Ch. 3 in [refAH], p. 52-196. | MR

[11] Lev (A.).— The covering number of the group PSL n (F), J. Algebra, 182, p. 60-84 (1996). | MR | Zbl

[12] Liebeck (M. W.), Shalev (A.).— Diameter of finite simple groups: sharp bounds and applications, Ann. of Math., 154, p. 383-406 (2001). | MR | Zbl

[13] Malle (G.), Matzat (B. H.).— Inverse Galois Theory, Springer-Verlag, addr Berlin, N.Y. (1999). | MR | Zbl

[14] Orevkov (S. Yu.).— Quasipositivity test via unitary representations of braid groups and its applications to real algebraic curves, J. of Knot Theory and Ramifications, 10, p. 1005-1023 (2001). | MR | Zbl

[15] Simpson (W.A.), Frame (J.S.).— The character tables for SL(3,q), SU(3,q 2 ), PSL(3,q), PSU(3,q 2 ), Canad. J. Math., 25, p. 486-494 (1973). | MR | Zbl

[16] Wall (G. E.) On the conjugacy classes in the unitary, symplectic and orthogonal groups, J. Austral. Math. Soc., 3, p. 1-62 (1963). | MR | Zbl

[17] Wall (G. E.).— Conjugacy classes in projective and special linear groups, Bull. Austral. Math. Soc., 22, p. 339-364 (1980). | MR | Zbl

Cité par Sources :