Geodesic
Width of extraspecial unipotent radical with respect to root elements
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 28, Tome 435 (2015), pp. 168-177 
I. M. Pevzner. Width of extraspecial unipotent radical with respect to root elements. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 28, Tome 435 (2015), pp. 168-177. http://geodesic.mathdoc.fr/item/ZNSL_2015_435_a8/
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Let $G=G(\Phi,K)$ be a Chevalley group of type $Ф$ over a field $K$, where $\Phi$ is a simply-laced root system. We study the extraspecial unipotent radical of $G$ and prove that any its element is a product of not more than three root elements. Moreover, we prove that any element of the radical is, possibly after a conjugation by an element of the Levi subgroup, a product of six elementary root elements.

[1] A. Borel, “Svoistva i lineinye predstavleniya grupp Shevalle”, Seminar po algebraicheskim gruppam, Mir, M., 1973, 9–59 | MR

[2] N. Burbaki, Gruppy i algebry Li, Glavy IV–VI, Mir, M., 1972 | MR

[3] N. Burbaki, Gruppy i algebry Li, Glavy VII–VIII, Mir, M., 1978 | MR

[4] N. A. Vavilov, A. Yu. Luzgarev, I. M. Pevzner, “Gruppa Shevalle tipa $\mathrm E_6$ v 27-mernom predstavlenii”, Zap. nauchn. semin. POMI, 338, 2006, 5–68 | MR | Zbl

[5] N. A. Vavilov, I. M. Pevzner, “Troiki dlinnykh kornevykh podgrupp”, Zap. nauchn. semin. POMI, 343, 2007, 54–83 | MR

[6] N. A. Vavilov, A. A. Semenov, “Dlinnye kornevye tory v gruppakh Shevalle”, Algebra i analiz, 24:3 (2012), 22–83 | MR | Zbl

[7] O. O'Mira, “Lektsii o lineinykh gruppakh”, Avtomorfizmy klassicheskikh grupp, Mir, M., 1976, 57–167 | MR

[8] O. O'Mira, Lektsii o simplekticheskikh gruppakh, Mir, M., 1979

[9] I. M. Pevzner, “Geometriya kornevykh elementov v gruppakh tipa $\mathrm E_6$”, Algebra i analiz, 23:3 (2011), 261–309 | MR | Zbl

[10] I. M. Pevzner, “Shirina grupp tipa $\mathrm E_6$ otnositelno mnozhestva kornevykh elementov. I”, Algebra i analiz, 23:5 (2011), 155–198 | MR

[11] I. M. Pevzner, “Shirina grupp tipa $\mathrm E_6$ otnositelno mnozhestva kornevykh elementov. II”, Zap. nauchn. semin. POMI, 386, 2011, 242–264 | MR

[12] I. M. Pevzner, “Shirina gruppy $\mathrm{GL}(6,K)$ otnositelno mnozhestva kvazikornevykh elementov”, Zap. nauchn. semin. POMI, 423, 2014, 183–204

[13] T. A. Springer, “Lineinye algebraicheskie gruppy”, Algebraicheskaya geometriya – 4, Itogi nauki i tekhn. Ser. Sovrem. problemy mat. Fundam. napravleniya, 55, VINITI, M., 1989, 5–136 | MR | Zbl

[14] R. Steinberg, Lektsii o gruppakh Shevalle, Mir, M., 1975 | MR

[15] Dzh. Khamfri, Lineinye algebraicheskie gruppy, Nauka, M., 1980 | MR

[16] Dzh. Khamfri, Vvedenie v teoriyu algebr Li i ikh predstavlenii, MTsNMO, M., 2003

[17] A. Cohen, A. Steinbach, R. Ushirobira, D. Wales, “Lie algebras generated by extremal elements”, J. Algebra, 236:1 (2001), 122–154 | DOI | MR | Zbl

[18] J. Dieudonné, “Sur les générateurs des groupes classiques”, Summa Brasil. Math., 3 (1955), 149–179 | MR

[19] T. A. Springer, Linear algebraic groups, Progress in Mathematics, 9, Birkhäuser Boston Inc., Boston, 1998 | MR | Zbl