Geodesic
Normalizer of an elementary net group associated with a non-split torus in the general linear group over a field
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 26, Tome 423 (2014), pp. 105-112 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

In this paper we compute the normalizer $N(\sigma)$ of an elementary net group $E(\sigma)$ associated with non-split maximal torus $T(d)$ in the general linear group $GL(n,k)$ over a field $k$ of odd characteristic. The non-split maximal torus $T=T(d)$ is provided by a radical extension $k(\sqrt[n]d)$ of degree $n$ of the ground field $k$ (minisotropic torus). 
@article{ZNSL_2014_423_a4,
     author = {N. A. Dzhusoeva and V. A. Koibaev},
     title = {Normalizer of an elementary net group associated with a~non-split torus in the general linear group over a~field},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {105--112},
     year = {2014},
     volume = {423},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2014_423_a4/}
}
TY  - JOUR
AU  - N. A. Dzhusoeva
AU  - V. A. Koibaev
TI  - Normalizer of an elementary net group associated with a non-split torus in the general linear group over a field
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2014
SP  - 105
EP  - 112
VL  - 423
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2014_423_a4/
LA  - ru
ID  - ZNSL_2014_423_a4
ER  - 
%0 Journal Article
%A N. A. Dzhusoeva
%A V. A. Koibaev
%T Normalizer of an elementary net group associated with a non-split torus in the general linear group over a field
%J Zapiski Nauchnykh Seminarov POMI
%D 2014
%P 105-112
%V 423
%U http://geodesic.mathdoc.fr/item/ZNSL_2014_423_a4/
%G ru
%F ZNSL_2014_423_a4
N. A. Dzhusoeva; V. A. Koibaev. Normalizer of an elementary net group associated with a non-split torus in the general linear group over a field. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 26, Tome 423 (2014), pp. 105-112. http://geodesic.mathdoc.fr/item/ZNSL_2014_423_a4/

[1] Z. I. Borevich, “Opisanie podgrupp polnoi lineinoi gruppy, soderzhaschikh gruppu diagonalnykh matrits”, Zap. nauchn. semin. LOMI, 64, 1976, 12–29 | MR | Zbl

[2] Z. I. Borevich, N. A. Vavilov, “Podgruppy polnoi lineinoi gruppy nad polulokalnym koltsom, soderzhaschie gruppu diagonalnykh matrits”, Tr. mat. in-ta AN SSSR, 148, 1978, 43–57 | MR | Zbl

[3] Z. I. Borevich, V. A. Koibaev, Chan Ngok Khoi, “Reshetki podgrupp v $GL(2,Q)$, soderzhaschikh nerasschepimyi tor”, Zap. nauchn. semin. POMI, 191, 1991, 24–43 | MR | Zbl

[4] N. A. Vavilov, “Podgruppy grupp Shevalle, soderzhaschie maksimalnyi tor”, Tr. Leningr. mat. ob-va, 1, 1990, 64–109 | MR

[5] N. A. Vavilov, “O podgruppakh rasschepimykh klassicheskikh grupp”, Tr. MIAN SSSR, 183, 1990, 29–42 | MR | Zbl

[6] N. A. Vavilov, E. V. Dybkova, “O podgruppakh polnoi simplekticheskoi gruppy, soderzhaschikh gruppu diagonalnykh matrits”, Zap. nauch. seminarov LOMI, 103, 1980, 31–47 ; “II”, Зап. науч. семинаров ЛОМИ, 132, 1983, 44–56 | MR | Zbl | MR

[7] N. A. Dzhusoeva, “Setevye gruppy, assotsiirovannye s torom”, Tezisy IX Mezhdunarodnoi shkoly-konferentsii po teorii grupp (Vladikavkaz, 9–15 iyulya 2012), 47

[8] N. A. Dzhusoeva, V. A. Koibaev, “Maksimalnye podgruppy, soderzhaschie tor, svyazannye s polem otnoshenii dedekindovoi oblasti”, Zap. nauchn. semin. POMI, 289, 2002, 149–153 | MR | Zbl

[9] N. A. Dzhusoeva, “Setevye koltsa normalizuemye torom”, Trudy IMM UrO RAN, 19, no. 3, 2013, 113–119

[10] V. A. Koibaev, “Podgruppy gruppy $GL(2,Q)$, soderzhaschie nerasschepimyi maksimalnyi tor”, Dokl. AN SSSR, 312:1 (1990), 36–38 | MR

[11] V. A. Koibaev, “Podgruppy gruppy $GL(2,K)$, soderzhaschie nerasschepimyi maksimalnyi tor”, Zap. nauchn. semin. POMI, 211, 1994, 136–145 | MR | Zbl

[12] V. A. Koibaev, “Transvektsii v podgruppakh polnoi lineinoi gruppy, soderzhaschikh nerasschepimyi maksimalnyi tor”, Algebra i analiz, 21:5 (2009), 70–86 | MR | Zbl

[13] V. A. Koibaev, A. V. Shilov, “Nadgruppy nerasschepimogo tora, modul transvektsii kotorykh sovpadaet s koltsom”, Mezhdunarodnaya konferentsiya “Algebra, Logika i Prilozheniya”, Krasnoyarsk, 2010, 49–50

[14] D. Z. Djokovic, “Subgroups of compact Lie groups containing a maximal torus are closed”, Proc. Amer. Math. Soc., 83:2 (1981), 431–432 | DOI | MR | Zbl

[15] W. M. Kantor, “Linear groups containing a Singer cycle”, J. Algebra, 62:1 (1980), 232–234 | DOI | MR | Zbl

[16] V. P. Platonov, “Subgroups of algebraic groups over local or a global field containing a maximal torus”, C. R. Acad. Sci. Paris, 318:10 (1994), 899–903 | MR | Zbl

[17] G. M. Seitz, “Subgroups of finite groups of Lie type”, J. Algebra, 61 (1979), 16–27 | DOI | MR | Zbl

[18] G. M. Seitz, “Root subgroups for maximal tori in finite groups of Lie type”, Pacif. J. Math., 106:1 (1983), 153–244 | DOI | MR | Zbl