Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 3, Tome 211 (1994), pp. 67-79
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A. A. Bongarenko. Arrangement of the subgroups that contain an unramified quadratic torus in the general linear group of degree 2 over a local number field ($p\ne2$). Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 3, Tome 211 (1994), pp. 67-79. http://geodesic.mathdoc.fr/item/ZNSL_1994_211_a3/
@article{ZNSL_1994_211_a3,
author = {A. A. Bongarenko},
title = {Arrangement of the subgroups that contain an unramified quadratic torus in the general linear group of degree~2 over a~local number field ($p\ne2$)},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {67--79},
year = {1994},
volume = {211},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1994_211_a3/}
}
TY - JOUR
AU - A. A. Bongarenko
TI - Arrangement of the subgroups that contain an unramified quadratic torus in the general linear group of degree 2 over a local number field ($p\ne2$)
JO - Zapiski Nauchnykh Seminarov POMI
PY - 1994
SP - 67
EP - 79
VL - 211
UR - http://geodesic.mathdoc.fr/item/ZNSL_1994_211_a3/
LA - ru
ID - ZNSL_1994_211_a3
ER -
%0 Journal Article
%A A. A. Bongarenko
%T Arrangement of the subgroups that contain an unramified quadratic torus in the general linear group of degree 2 over a local number field ($p\ne2$)
%J Zapiski Nauchnykh Seminarov POMI
%D 1994
%P 67-79
%V 211
%U http://geodesic.mathdoc.fr/item/ZNSL_1994_211_a3/
%G ru
%F ZNSL_1994_211_a3
Let $k$ be a nondyadic local number field and let $K=k(\sqrt\omega)$ be its unramifield quadratic extension. A complete description is suggested for the intermediate subgroups of the general linear group $\mathrm{G=GL}(2,k)$ of degree 2 over the field $k$ that contain the nonsplit maximal torus $T=T(\omega)$ (i.e., the image in $\mathrm G$ of the multiplicative group $K^*$ of the field $K$ under the regular embedding). In particular, the torus $T(\omega)$ is polynormal in $\mathrm{GL}(2,k)$. Bibliography: 11 titles.
