On the Cohomology and K-Theory of the General Linear Groups Over a Finite Field

1972 ◽  
Vol 96 (3) ◽  
pp. 552 ◽  
Author(s):  
Daniel Quillen
Keyword(s):  
Finite Field ◽  
General Linear ◽  
Linear Groups ◽  
General Linear Groups ◽  
K Theory

Intersection graphs of general linear groups

2020 ◽  
pp. 2150039
Author(s):  
Mai Hoang Bien ◽  
Do Hoang Viet
Keyword(s):  
Finite Field ◽  
Linear Group ◽  
General Linear Group ◽  
Undirected Graph ◽  
Intersection Graph ◽  
General Linear ◽  
Linear Groups ◽  
Intersection Graphs ◽  
General Linear Groups ◽  
Vertex Set

Let [Formula: see text] be a field and [Formula: see text] the general linear group of degree [Formula: see text] over [Formula: see text]. The intersection graph [Formula: see text] of [Formula: see text] is a simple undirected graph whose vertex set includes all nontrivial proper subgroups of [Formula: see text]. Two vertices [Formula: see text] and [Formula: see text] of [Formula: see text] are adjacent if [Formula: see text] and [Formula: see text]. In this paper, we show that if [Formula: see text] is a finite field containing at least three elements, then the diameter [Formula: see text] is [Formula: see text] or [Formula: see text]. We also classify [Formula: see text] according to [Formula: see text]. In case [Formula: see text] is infinite, we prove that [Formula: see text] is one-ended of diameter 2 and its unique end is thick.

scholarly journals general linear groups

1997 ◽  
Vol 90 (3) ◽  
pp. 549-576 ◽  
Author(s):  
Avner Ash ◽  
Mark McConnell
Keyword(s):  
General Linear ◽  
Linear Groups ◽  
General Linear Groups
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