A conjugacy theorem for subgroups of $\mathrm{SL}_n$ containing the group of diagonal matrices
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 7, Tome 272 (2000), pp. 177-185
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Let $R$ be a commutative local ring. It is proved that if $n\ge3$ and the residue field of $R$ contains at least $3n+2$ elements, then the subgroup of diagonal matrices in the special linear group of degree $n$ over $R$ is pronormal. For semilocal rings with the same restrictions on residue fields this subgroup is paranormal.
@article{ZNSL_2000_272_a8,
author = {A. E. Egorov and A. A. Panin},
title = {A conjugacy theorem for subgroups of $\mathrm{SL}_n$ containing the group of diagonal matrices},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {177--185},
publisher = {mathdoc},
volume = {272},
year = {2000},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2000_272_a8/}
}
TY - JOUR
AU - A. E. Egorov
AU - A. A. Panin
TI - A conjugacy theorem for subgroups of $\mathrm{SL}_n$ containing the group of diagonal matrices
JO - Zapiski Nauchnykh Seminarov POMI
PY - 2000
SP - 177
EP - 185
VL - 272
PB - mathdoc
UR - http://geodesic.mathdoc.fr/item/ZNSL_2000_272_a8/
LA - ru
ID - ZNSL_2000_272_a8
ER -
A. E. Egorov; A. A. Panin. A conjugacy theorem for subgroups of $\mathrm{SL}_n$ containing the group of diagonal matrices. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 7, Tome 272 (2000), pp. 177-185. http://geodesic.mathdoc.fr/item/ZNSL_2000_272_a8/