Geodesic
Garlands containing the general linear groups over a intermediate field
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 5, Tome 236 (1997), pp. 34-41 
Z. I. Borevich; V. A. Koibaev; I. V. Lavrent'ev. Garlands containing the general linear groups over a intermediate field. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 5, Tome 236 (1997), pp. 34-41. http://geodesic.mathdoc.fr/item/ZNSL_1997_236_a3/
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     title = {Garlands containing the general linear groups over a~intermediate field},
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     year = {1997},
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}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Let $K/k$ be a finite extension of fields with intermediate subfield $L$ and let $H=$GL$_L(k)$ be the general linear group of the all $L$-linear invertible mappings of the vector space of the field $k$ over $L$. It is proved that the intermediate between GL$_k(K)^H$ and the normalizae of $H$ subgroups form a goarland.

[1] A. Kh. Al Khamad, Girlyandy v lineinykh gruppakh, svyazannye s koltsami normirovaniya, Diss. kand.f.-m.n., SPb., 1992

[2] E. Artin, Geometricheskaya Algebra, Nauka, M., 1969, 283 pp. | MR | Zbl

[3] V. A. Koibaev, “Normalizator gruppy avtomorfizmov modulya, voznikayuschego pri rasshirenii osnovnogo koltsa”, Zap. nauchn. semin. LOMI, 211, 1994, 133–135 | MR | Zbl

[4] D. A. Suprunenko, Gruppy matrits, Nauka, M., 1972 | MR