Arrangement of the subgroups that contain an unramified quadratic torus in the general linear group of degree 2 over a local number field ($p=2$)
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 3, Tome 211 (1994), pp. 80-90
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Let $k$ be a dyadic local number field and let $K=k(\sqrt d)$ be an unramified 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 $T=T(d)$ (i.e., the image in $\mathrm G$ of the multiplicative group $K^*$ of the field $K$ under the regular embedding). In particular, the torus $T(d)$ is polynormal in $\mathrm{GL}(2,k)$. Bibliography: 11 titles.
@article{ZNSL_1994_211_a4,
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~($p=2$)},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {80--90},
year = {1994},
volume = {211},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1994_211_a4/}
}
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%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 ($p=2$) %J Zapiski Nauchnykh Seminarov POMI %D 1994 %P 80-90 %V 211 %U http://geodesic.mathdoc.fr/item/ZNSL_1994_211_a4/ %G ru %F ZNSL_1994_211_a4
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 ($p=2$). Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 3, Tome 211 (1994), pp. 80-90. http://geodesic.mathdoc.fr/item/ZNSL_1994_211_a4/