Subgroups of Chevalley Groups Over Rings

2021 ◽  
Vol 252 (6) ◽  
pp. 829-840
Author(s):  
R. Lubkov ◽  
A. Stepanov
Keyword(s):  
Chevalley Groups

scholarly journals 1-Cohomology of Chevalley groups

1989 ◽  
Vol 127 (2) ◽  
pp. 353-372 ◽  
Author(s):  
Helmut Völklein
Keyword(s):  
Chevalley Groups

Elements of Order Coxeter Number +1 in Chevalley Groups

1982 ◽  
Vol 34 (4) ◽  
pp. 945-951 ◽  
Author(s):  
Bomshik Chang
Keyword(s):  
Weyl Group ◽  
Chevalley Group ◽  
Trivial Solution ◽  
Affirmative Answer ◽  
Chevalley Groups ◽  
General Solutions ◽  
Coxeter Number ◽  
Image Position

Following the notation and the definitions in [1], let L(K) be the Chevalley group of type L over a field K, W the Weyl group of L and h the Coxeter number, i.e., the order of Coxeter elements of W. In a letter to the author, John McKay asked the following question: If h + 1 is a prime, is there an element of order h + 1 in L(C)? In this note we give an affirmative answer to this question by constructing an element of order h + 1 (prime or otherwise) in the subgroup Lz = 〈xτ(1)|r ∈ Φ〉 of L(K), for any K.Our problem has an immediate solution when L = An. In this case h = n + 1 and the (n + l) × (n + l) matrixhas order 2(h + 1) in SLn+1(K). This seemingly trivial solution turns out to be a prototype of general solutions in the following sense.

scholarly journals Maximal subgroups and automorphisms of Chevalley groups

1977 ◽  
Vol 71 (2) ◽  
pp. 365-403 ◽  
Author(s):  
N. Burgoyne ◽  
Robert Griess ◽  
Richard Lyons
Keyword(s):  
Maximal Subgroups ◽  
Chevalley Groups

scholarly journals Faithful representations of Chevalley groups over quotient rings of non-Archimedean local fields

2017 ◽  
Vol 11 (1) ◽  
pp. 57-74 ◽  
Author(s):  
Mohammad Bardestani ◽  
Camelia Karimianpour ◽  
Keivan Mallahi-Karai ◽  
Hadi Salmasian
Keyword(s):  
Local Fields ◽  
Chevalley Groups ◽  
Quotient Rings

scholarly journals On Pairs of Additive Subgroups Associated with Intermediate Subgroups of Groups of Lie Type over Nonperfect Fields

2021 ◽  
Vol 14 (5) ◽  
pp. 604-610
Author(s):  
Yakov N. Nuzhin ◽  
Keyword(s):  
Algebraic Extension ◽  
Chevalley Groups ◽  
Intermediate Subgroups ◽  
Diagonal Subgroup ◽  
Groups Of Lie Type ◽  
Nonperfect Field

The author has previously (Trudy IMM UrO RAN, 19(2013), no. 3) described the groups lying between twisted Chevalley groups G(K) and G(F) of type 2Al, 2Dl, 2E6, 3D4 in the case when the larger field F is an algebraic extension of the smaller nonperfect field K of exceptional characteristic for the group G(F) (characteristics 2 and 3 for the type 3D4 and only 2 for other types). It turned out that apart from, perhaps, the type 2Dl, such intermediate subgroups are standard, that is, they are exhausted by the groups G(P)H for some intermediate subfield P, K ⊆ P ⊆ F, and of the diagonal subgroup H normalizing the group G(P). In this note, it is established that intermediate subgroups are also standard for the type 2Dl

Bruhat decomposition for long root tori in Chevalley groups

1991 ◽  
Vol 57 (6) ◽  
pp. 3453-3458 ◽  
Author(s):  
N. A. Vavilov ◽  
A. A. Semenov
Keyword(s):  
Bruhat Decomposition ◽  
Chevalley Groups
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