Geodesic
Classes of Conjugate Involutions of Symplectic Groups over Fields of Even Order and Related Questions
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 1 (2008) no. 3, pp. 324-328.

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

We use an analogue of the Suzuki form in $PSL(n,q)$ in order to find representatives of conjugate involution classes of symplectic groups $Sp(2n,q)$ over fields of any even order. Let $\tau$ be an involution of a group $G$ and $ccw(G,\tau)$ denote the number of all conjugate and commutative involutions for $\tau$. We establish an uppen bound for this number in the case of $Sp(2n,q)$.
Keywords: symplectic group, involution. 
@article{JSFU_2008_1_3_a11,
     author = {Oksana V. Radchenko},
     title = {Classes of {Conjugate} {Involutions} of {Symplectic} {Groups} over {Fields} of {Even} {Order} and {Related} {Questions}},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
     pages = {324--328},
     publisher = {mathdoc},
     volume = {1},
     number = {3},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2008_1_3_a11/}
}
TY  - JOUR
AU  - Oksana V. Radchenko
TI  - Classes of Conjugate Involutions of Symplectic Groups over Fields of Even Order and Related Questions
JO  - Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
PY  - 2008
SP  - 324
EP  - 328
VL  - 1
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/JSFU_2008_1_3_a11/
LA  - ru
ID  - JSFU_2008_1_3_a11
ER  - 
%0 Journal Article
%A Oksana V. Radchenko
%T Classes of Conjugate Involutions of Symplectic Groups over Fields of Even Order and Related Questions
%J Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika
%D 2008
%P 324-328
%V 1
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/JSFU_2008_1_3_a11/
%G ru
%F JSFU_2008_1_3_a11
Oksana V. Radchenko. Classes of Conjugate Involutions of Symplectic Groups over Fields of Even Order and Related Questions. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 1 (2008) no. 3, pp. 324-328. http://geodesic.mathdoc.fr/item/JSFU_2008_1_3_a11/

[1] M. Suzuki, “Characterizations of linear groups”, Bull. AMS, 75 (1969), 1043–1091 | DOI | MR | Zbl

[2] M. Aschbacher, G. M. Seitz, “Involutions in chevalley groups over fields of even order”, Nagoya Math. J., 63 (1976), 1–91 | MR | Zbl

[3] R. W. Carter, Simple groups of Lie type, Wiley and Sons, New York, 1972 | MR | Zbl

[4] V. M. Levchuk, G. S. Suleimanova, “Normalnoe stroenie unipotentnoi podgruppy gruppy lieva tipa i smezhnye voprosy”, Dokl. RAN, 419:5 (2008), 595–598

[5] V. M. Levchuk, “Growth of the intersection of the centralizer of an involution and its class of conjugated elements in finite simple groups”, Proceed. Int. Conf. “Antalya Algebra Days VIII” (17-21 May, 2006), Bilgi Univ., Istanbul, 2006, 26

[6] V. P. Shunkov, “Gruppy s involyutsiyami”, Cb. tezisov dokl. mezhdunarod. sem. po teorii grupp, IMM UrO RAN, Ekaterinburg, 2001, 245–246

[7] P. Brauer, “O stroenii grupp konechnogo poryadka”, Mezhdunarodnyi matematicheskii kongress v Amsterdame 1954 g., Fizmatgiz, M., 1961, 23–35

[8] O. V. Golovanova, V. M. Levchuk, “Zavisimost poryadkov konechnoi prostoi gruppy i peresecheniya tsentralizatora i klassa sopryazhennykh elementov involyutsii”, Izvestiya Gomelskogo gosudarstvennogo universiteta im. F. Skoriny, 3:36 (2006), 124–130

[9] O. V. Radchenko, “Sopryazhenno-kommutativnaya shirina involyutsii gruppy s odnim klassom sopryazhennykh involyutsii”, Vestnik KrasGU, 2006, no. 9, 64–69

[10] A. G. Likharev, Ogranichennost sopryazhenno-kommutativnoi shiriny involyutsii v gruppakh Shevalle, Preprint No 4, IVM SO RAN, Krasnoyarsk, 2006

[11] O. V. Golovanova, “Parametry vlozheniya involyutsii konechnykh prostykh grupp lieva tipa ranga 1”, Vestnik KrasGU, 2006, no. 4, 49–54

[12] V. M. Levchuk, “Avtomorfizmy unipotentnykh podgrupp grupp Shevalle”, Algebra i logika, 29:3 (1990), 315–338 | MR | Zbl

[13] N. Burbaki, Gruppy i algebry Li, gl. IV–VI, Mir, M., 1982 | MR