Covering numbers for Chevalley groups

1999 ◽  
Vol 111 (1) ◽  
pp. 339-372 ◽  
Author(s):  
Erich W. Ellers ◽  
Nikolai Gordeev ◽  
Marcel Herzog
Keyword(s):  
Chevalley Groups ◽  
Covering Numbers

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
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