TY - JOUR

T1 - Parabolic subgroups of twisted Chevalley groups over a semilocal ring

AU - Vavilov, N. A.

N1 - Copyright: Copyright 2007 Elsevier B.V., All rights reserved.

PY - 1982/5

Y1 - 1982/5

N2 - It is shown that, under minor additional assumptions, the standard parabolic subgroups of a Chevalley group Gρ(Φ, R) of twisted type Φ=Al, l odd, Dl, E6 over a commutative semilocal ring R with involution ρ are in one-to-one correspondence with the ρ-invariant parabolic nets of ideals of R of type Φ, i.e., with the sets[Figure not available: see fulltext.], of ideals σα of R such that: (l)[Figure not available: see fulltext.][Figure not available: see fulltext.] whenever[Figure not available: see fulltext.]; (2)ρσα=σρα for all α; (3) σα=R for α > 0. For Chevalley groups of normal types, analogous results were obtained in Ref. Zh. Mat. 1976, 10A151; 1977, 10A 301; 1978, 6A476.

AB - It is shown that, under minor additional assumptions, the standard parabolic subgroups of a Chevalley group Gρ(Φ, R) of twisted type Φ=Al, l odd, Dl, E6 over a commutative semilocal ring R with involution ρ are in one-to-one correspondence with the ρ-invariant parabolic nets of ideals of R of type Φ, i.e., with the sets[Figure not available: see fulltext.], of ideals σα of R such that: (l)[Figure not available: see fulltext.][Figure not available: see fulltext.] whenever[Figure not available: see fulltext.]; (2)ρσα=σρα for all α; (3) σα=R for α > 0. For Chevalley groups of normal types, analogous results were obtained in Ref. Zh. Mat. 1976, 10A151; 1977, 10A 301; 1978, 6A476.

UR - http://www.scopus.com/inward/record.url?scp=34250233151&partnerID=8YFLogxK

U2 - 10.1007/BF01476110

DO - 10.1007/BF01476110

M3 - Article

AN - SCOPUS:34250233151

VL - 19

SP - 987

EP - 998

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 1

ER -