Some cohomology of finite general linear groups
David Sprehn

TL;DR
This paper proves non-vanishing of certain cohomology groups for finite groups of Lie type over finite fields, providing explicit constructions and calculations for specific cases, advancing understanding of their algebraic structure.
Contribution
It establishes non-zero cohomology in specific degrees for finite Lie groups and explicitly constructs non-zero elements, with detailed calculations for general linear groups under certain conditions.
Findings
Non-zero cohomology in degree r(2p-3) for groups with Coxeter number ≤ p
Explicit construction of non-zero cohomology classes
Cohomology calculations for GL_n over finite fields when p=2 or r=1
Abstract
We prove that the degree cohomology of any (untwisted) finite group of Lie type over , with coefficients in characteristic , is nonzero as long as its Coxeter number is at most . We do this by providing a simple explicit construction of a nonzero element. Furthermore, for the groups , when or , we calculate the cohomology in degree , for all .
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Finite Group Theory Research
