@article{MT_2024_27_2_a3,
author = {A. A. Galt},
title = {Structure of normalizers of maximal tori in groups of {Lie} type},
journal = {Matemati\v{c}eskie trudy},
pages = {62--98},
year = {2024},
volume = {27},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MT_2024_27_2_a3/}
}
A. A. Galt. Structure of normalizers of maximal tori in groups of Lie type. Matematičeskie trudy, Tome 27 (2024) no. 2, pp. 62-98. http://geodesic.mathdoc.fr/item/MT_2024_27_2_a3/
[1] Carter R. W., Finite groups of Lie type: sonjugacy classes and complex characters, John Wiley and Sons, New York etc., 1985 | MR
[2] Carter R. W., “Centralizers of semisimple elements in finite groups of Lie type”, Proc. Lond. Math. Soc., 37 (1978), 491–507 | DOI | MR | Zbl
[3] Carter R. W., “Centralizers of semisimple elements in the finite classical groups”, Proc. Lond. Math. Soc., 42:1 (1981), 1–41 | DOI | MR | Zbl
[4] Buturlakin A. A., Grechkoseeva M. A., “The cyclic structure of maximal tori of the finite classical groups”, Algebra and Logic, 46:2 (2007), 73–89 | DOI | MR | Zbl
[5] Deriziotis D. I., Fakiolas A. P., “The maximal tori in the finite Chevalley groups of type $E_6,E_7$ and $E_8$”, Comm. Algebra, 19:3 (1991), 889–903 | DOI | MR | Zbl
[6] Deriziotis D. I., Michler G. O., “Character table and blocks of finite simple triality groups ${}^3D_4(q)$”, Trans. Amer. Math. Soc., 303:1 (1987), 39–70 | MR | Zbl
[7] Shinoda K., “The conjugacy classes of Chevalley groups of type $F_4$ over finite fields of characteristic 2”, Journal Of The Faculty Of Science, The University Of Tokyo, 21 (1974), 133–159 | MR | Zbl
[8] Shinoda K., “The conjugacy classes of the finite Ree groups of type $F_4$”, Journal Of The Faculty Of Science, The University Of Tokyo, 22 (1975), 1–15 | MR | Zbl
[9] Shoji T., “The conjugacy classes of Chevalley groups of type $F_4$ over finite fields of characteristic $p\neq2$”, J. Fac. Sci. Univ. Tokyo, 21 (1974), 1–17 | DOI | MR | Zbl
[10] Lawther R., “The action of $F_4(q)$ on cosets of $B_4(q)$”, J. Algebra, 212 (1999), 79–118 | DOI | MR | Zbl
[11] Fleischmann P., Janiszczak I., “The semisimple conjugacy classes of finite groups of Lie type $E_6$ and $E_7$”, Comm. Algebra, 21:1 (1993), 93–161 | DOI | MR | Zbl
[12] Fleischmann P., Janiszczak I., “The semisimple conjugacy classes and the generic class number of the finite simple groups of Lie type $E_8$”, Comm. Algebra, 22:6 (1994), 2221–2303 | DOI | MR | Zbl
[13] W. M. Kantor W. M., Seress A., “Prime power graphs for groups of Lie type”, J. Algebra, 247 (2002), 370–434 | DOI | MR | Zbl
[14] Gager P., Maximal tori in finite groups of Lie type, PhD Thesis, University of Warwick, 1973
[15] Malle G., Testerman D., Linear Algebraic Groups and Finite Groups of Lie Type, Cambridge University Press, 2011 | MR | Zbl
[16] Tits J., “Normalisateurs de tores I. Groupes de Coxeter Étendus”, J. Algebra, 4 (1966), 96–116 | DOI | MR | Zbl
[17] Curtis M., Wiederhold A., Williams B., “Normalizers of maximal tori, Localization in group theory and homotopy theory, and related topics”, Sympos., Battelle Seattle Res. Center (Seattle, Wash.), Lecture Notes in Math., 418, Springer, Berlin, 1974, 31–47 | DOI | MR
[18] Adams J., He X., “Lifting of elements of Weyl groups”, J. Algebra, 485 (2017), 142–165 | DOI | MR | Zbl
[19] Zaremsky Matthew C. B., “Representatives of elliptic Weyl group elements in algebraic groups”, J. Group Theory, 17:1 (2014), 49–71 | DOI | MR | Zbl
[20] Reeder M., Levy P., Yu J.-K., Gross B. H., “Gradings of positive rank on simple Lie algebras”, Transform. Groups, 17:4 (2012), 1123–1190 | DOI | MR | Zbl
[21] Lusztig G., “Lifting involutions in a Weyl group to the torus normalizer”, Represent.Th., 22 (2018), 27–44 | DOI | MR | Zbl
[22] Adrian M., “Lifting involutions in a Weyl group to the normalizer of the torus”, Proc. Amer. Math. Soc., 150:11 (2022), 4989–4994 | DOI | MR | Zbl
[23] Humphreys J., Linear Algebraic Groups, Springer, New York, NY, 1975 | MR | Zbl
[24] Kondrat'ev A. S., “Subgroups of finite Chevalley groups”, Russian Math. Surveys, 41:1 (1986), 65–118 | DOI | Zbl
[25] Carter R. W., Simple groups of Lie type, John Wiley and Sons, London etc., 1972 | MR | Zbl
[26] Vavilov N. A., “Do it yourself structure constants for Lie algebras of types $E_l$”, J. Math. Sci. (N.Y.), 120:4 (2004), 1513–1548 | DOI | MR
[27] Gorenstein D., Lyons R., Solomon R., The classification of the finite simple groups. Number 3. Part I. Chapter A. Almost simple $K$-groups, Mathematical Surveys and Monographs, 40, no. 3, American Mathematical Society, Providence, RI, 1998 | MR
[28] Baykalov A. A., “On algebraic normalisers of maximal tori in simple groups of Lie type”, Journal of Group Theory, 2024 | DOI | MR | Zbl
[29] Gal't A. A., “On the splitting of the normalizer of a maximal torus in symplectic groups”, Izv. Math., 78:3 (2014), 443–458 | DOI | DOI | MR | Zbl
[30] Galt A. A., “On splitting of the normalizer of a maximal torus in linear groups”, J. Algebra Appl., 14:7 (2015), 1550114, 20 pp. | DOI | MR | Zbl
[31] Galt A. A., Staroletov A. M., “Splitting of Normalizers of Maximal Tori in Finite Groups of Lie Type”, Algebra and Logic, 62:1 (2023), 22–40 | DOI | MR
[32] Galt A. A., “On splitting of the normalizer of a maximal torus in orthogonal groups”, J. Algebra Appl., 16:9 (2017), 1750174, 23 pp. | DOI | MR
[33] Galt A. A., Staroletov A. M., “On splitting of the normalizer of a maximal Torus in $E_6(q)$”, Algebra Colloq., 26:2 (2019), 329–350 | DOI | DOI | MR
[34] Galt A. A., Staroletov A. M., “On splitting of the normalizer of a maximal Torus in $E_6(q)$”, Algebra Colloq., 26:2 (2019), 329–350 | DOI | MR
[35] Galt A. A., Staroletov A. M., “On splitting of the normalizer of a maximal torus in $E_7(q)$ and $E_8(q)$”, Siberian Adv. Math., 31:4 (2021), 244–282 | DOI | MR
[36] Galt A. A., Staroletov A. M., “Minimal supplements of maximal tori in their normalizers for the groups $F_4(q)$”, Izv. Math., 86:1 (2022), 126–149 | DOI | DOI | MR
[37] Adrian M., “The Sections of the Weyl Group”, Int. Math. Res. Not., 10 (2022), 7654–7693 | DOI | MR
[38] Gerasimov A. A., Lebedev D. R., Oblezin S. V., “Normalizers of maximal tori in classical Lie groups”, Algebra i Analiz, 35:2 (2023), 1–54