Geodesic
On the intermediate subgroups of the general linear group containing group of quaternions
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 5, Tome 236 (1997), pp. 13-22 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

Let $G=G(2,K)$ be a general linear group over a quadratic extention $K$ of the field $F$ (char $F\ne2$) and let $D=(\frac{a,b}F)$ be an algebra of quaternions with division containing $F$. The subgroups $H$ of $G$ containing a matrix realisation of multiplicative group $D^*$ of the algebra $D$ considered. The discription of the rings of multipliers of the intermediate subgroups is gived. 
@article{ZNSL_1997_236_a1,
     author = {A. A. Bongarenko},
     title = {On the intermediate subgroups of the general linear group containing group of quaternions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {13--22},
     year = {1997},
     volume = {236},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1997_236_a1/}
}
TY  - JOUR
AU  - A. A. Bongarenko
TI  - On the intermediate subgroups of the general linear group containing group of quaternions
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 1997
SP  - 13
EP  - 22
VL  - 236
UR  - http://geodesic.mathdoc.fr/item/ZNSL_1997_236_a1/
LA  - ru
ID  - ZNSL_1997_236_a1
ER  - 
%0 Journal Article
%A A. A. Bongarenko
%T On the intermediate subgroups of the general linear group containing group of quaternions
%J Zapiski Nauchnykh Seminarov POMI
%D 1997
%P 13-22
%V 236
%U http://geodesic.mathdoc.fr/item/ZNSL_1997_236_a1/
%G ru
%F ZNSL_1997_236_a1
A. A. Bongarenko. On the intermediate subgroups of the general linear group containing group of quaternions. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 5, Tome 236 (1997), pp. 13-22. http://geodesic.mathdoc.fr/item/ZNSL_1997_236_a1/

[1] A. Kh. Al Khamad, A. A. Bondarenko, Z. I. Borevich, “Normalizator gruppy “diagonalnykh” avtomorfizmov v algebrakh nad kommutativnym koltsom”, Zap. nauchn. semin. POMI, 191, 1991, 5–8 | MR | Zbl

[2] A. Kh. Al Khamad, Girlyandy v lineinykh gruppakh, svyazannye s koltsami normirovaniya, Kand. diss., SPb., 1992

[3] M. S. Ba, Z. I. Borevich,, “O raspolozhenii promezhutochnykh podgrupp”, Koltsa i lineinye gruppy, Sb. nauchn. trudov, Krasnodar, 1988, 14–41 | MR

[4] A. A. Bondarenko, “Raspolozhenie podgrupp, soderzhaschikh nerazvetvlennyi tor v polnoi lineinoi gruppe stepeni 2 nad lokalnym chislovym polem $(p\ne2)$”, Zap. nauchn. semin. POMI, 211, 1994, 67–79 | MR

[5] A. A. Bondarenko, “Raspolozhenie podgrupp, soderzhaschikh nerazvetvlennyi tor v polnoi lineinoi gruppe stepeni 2 nad lokalnym chislovym polem $(p=2)$”, Zap. nauchn. semin. POMI, 221, 1994, 80–90 | MR

[6] A. A. Bondarenko, “Raspolozhenie podgrupp, soderzhaschikh razvetvlennyi kvadratichnyi tor, v polnoi lineinoi gruppe stepeni 2 nad lokalnym chislovym polem $(p\ne2)$”, Vestn. SPbGU, Ser. 1, Vyp. 4, 1993, no. 22, 7–15 | Zbl

[7] Z. I. Borevich, “O raspolozhenii podgrupp”, Zap. nauchn. semin. LOMI, 94, 1979, 5–12 | MR | Zbl

[8] Z. I. Borevich, V. A. Koibaev, Chan Ngok Khai, “Reshetki podgrupp v $GL(2,Q)$, soderzhaschikh nerasscheplennyi tor”, Zap. nauchn. semin. LOMI, 191, 1991, 24–43 | Zbl

[9] Z. I. Borevich, V. A. Koibaev, “O koltsakh mnozhitelei, svyazannykh s promezhutochnymi podgruppami dlya kvadratichnogo tora”, Vestn. SPbGU, Ser. 1, 1993, no. 2, 5–10 | MR | Zbl

[10] Z. I. Borevich, O. N. Matsedonskaya, “O reshetke podgrupp”, Zap. nauchn. semin. LOMI, 103, 1980, 13–19 | MR | Zbl

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

[12] V. A. Koibaev, “Podgruppy grupp $GL(2,k)$, soderzhaschie nerasschepimyi maksimalnyi tor”, Zap. nauchn. semin. POMI, 221, 1994, 136–145 | MR

[13] V. A. Koibaev, “Normalizator gruppy avtomorfizmov modulya, voznikayuschego pri rasshirenii osnovnogo koltsa”, Zap. nauchn. semin. POMI, 221, 1994, 133–135 | MR

[14] R. Pirs, Assotsiativnye algebry, M., 1986 | MR