scholarly journals Quasi-hereditary quotients of finite Chevalley groups and Frobenius kernels

2005 ◽  
Vol 56 (1) ◽  
pp. 111-121
Author(s):  
M. de Visscher
Keyword(s):  
Chevalley Groups ◽  
Frobenius Kernels

scholarly journals On comparing the cohomology of algebraic groups, finite Chevalley groups and Frobenius kernels

2001 ◽  
Vol 163 (2) ◽  
pp. 119-146 ◽  
Author(s):  
Christopher P. Bendel ◽  
Daniel K. Nakano ◽  
Cornelius Pillen
Keyword(s):  
Algebraic Groups ◽  
Chevalley Groups ◽  
Frobenius Kernels

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
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