AN OVERVIEW ON THE CLASSIFICATION OF FINITE GROUPS OF LIE TYPE

MONA LINKMANN

Abstract: The finite groups of Lie type are analogues over a finite field of the simple Lie groups over ℝ or ℂ. They arise as groups of rational points of affine connected reductive algebraic groups defined over a finite field 𝔽_{∥} of q = p^{e} elements, p being a prime and e ∈ ℕ, or in other words, they are described as the fix point groups with respect to the Frobenius morphism, the square or the cube of the Frobenius morphism of the given affine connected reductive algebraic group. Using the classification of affine connected reductive algebraic group over an algebraically closed field, one can also classify the finite groups of Lie type.