Primitive parabolic permutation representations for finite simple orthogonal groups in odd dimensions
Algebra i logika, Tome 49 (2010) no. 5, pp. 615-629.

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Ranks, degrees, subdegrees, and double stabilizers of permutation representations for finite simple orthogonal groups in odd dimensions are defined on cosets with respect to maximal parabolic subgroups.
Keywords: permutation representation, parabolic subgroup, finite simple group, classical group, isotropic subspace.
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V. V. Korableva. Primitive parabolic permutation representations for finite simple orthogonal groups in odd dimensions. Algebra i logika, Tome 49 (2010) no. 5, pp. 615-629. http://geodesic.mathdoc.fr/item/AL_2010_49_5_a2/

[1] V. D. Mazurov, “Minimalnye podstanovochnye predstavleniya konechnykh prostykh klassicheskikh grupp. Spetsialnye lineinye, simplekticheskie i unitarnye gruppy”, Algebra i logika, 32:3 (1993), 267–287 | MR | Zbl

[2] A. V. Bacilev, V. D. Mazurov, “Minimalnye podstanovochnye predstavleniya konechnykh prostykh ortogonalnykh grupp”, Algebra i logika, 33:6 (1994), 603–627 | MR

[3] A. V. Bacilev, “Minimalnye podstanovochnye predstavleniya konechnykh prostykh isklyuchitelnykh grupp tipa $G_2$ i $F_4$”, Algebra i logika, 35:6 (1996), 663–684 | MR

[4] A. V. Bacilev, “Minimalnye podstanovochnye predstavleniya konechnykh prostykh isklyuchitelnykh grupp tipa $E_6$, $E_7$ i $E_8$”, Algebra i logika, 36:5 (1997), 518–530 | MR

[5] A. V. Vasilev, “Minimalnye podstanovochnye predstavleniya konechnykh prostykh isklyuchitelnykh grupp skruchennogo tipa”, Algebra i logika, 37:1 (1998), 17–35 | MR

[6] M. A. Grechkoseeva, “O minimalnykh podstanovochnykh predstavleniyakh klassicheskikh prostykh grupp”, Sib. matem. zh., 44:3 (2003), 560–586 | MR | Zbl

[7] V. V. Korableva, “Parabolicheskie podstanovochnye predstavleniya gruppy $F_4(q)$”, Tr. In-ta matem. mekh. UrO RAN, 5, 1998, 39–59 | Zbl

[8] V. V. orableva, “Parabolicheskie podstanovochnye predstavleniya grupp $E_6(q)$ i $E_7(q)$”, Kombinatornye i vychislitelnye metody v matematike, OmGU, Omsk, 1999, 160–189

[9] V. V. Korableva, Parabolicheskie podstanovochnye predstavleniya grupp $E_8(q)$, dep. v VINITI, 29.10.99, No 3224-B99, Chelyab. gos. un-t, 221 pp.

[10] V. V. Korableva, “Parabolicheskie podstanovochnye predstavleniya grupp $^2F_4(q)$ i $^3D4(q^3)$”, Matem. zametki, 67:1 (2000), 69–76 | MR | Zbl

[11] V. V. Korableva, “Parabolicheskie podstanovochnye predstavleniya grupp $^2E_6(q^2)$”, Matem. zametki, 67:6 (2000), 899–912 | MR | Zbl

[12] V. V. Korableva, “Rangi primitivnykh parabolicheskikh podstanovochnykh predstavlenii klassicheskikh grupp lievskogo tipa $A_l(q)$”, Tr. In-ta matem. mekh. UrO RAN, 7, no. 2, 2001, 188–193 | MR | Zbl

[13] V. V. Korableva, “Primitivnye parabolicheskie podstanovochnye predstavleniya prostykh grupp $A_l(q)$”, Tr. In-ta matem. mekh. UrO RAN, 14, no. 4, 2008, 70–81

[14] V. V. Korableva, “Primitivnye parabolicheskie podstanovochnye predstavleniya konechnykh spetsialnykh lineinykh i unitarnykh grupp”, Tr. In-ta matem. mekh. UrO RAN, 15, no. 2, 2009, 114–124

[15] V. V. Korableva, “Primitivnye parabolicheskie podstanovochnye predstavleniya konechnykh simplekticheskikh grupp”, Algebra i logika, 49:3 (2010), 366–378

[16] V. V. Korableva, “Rangi primitivnykh parabolicheskikh podstanovochnykh predstavlenii prostykh grupp $B_l(q)$, $C_l(q)$ i $D_l(q)$”, Sib. matem. zh., 49:2 (2008), 340–356 | MR | Zbl

[17] P. B. Kleidman, M. Liebeck, The subgroups structure of finite classical groups, Lond. Math. Soc. Lect. Note Ser., 129, Cambridge Univ. Press, Cambridge etc., 1990 | MR | Zbl