Isomorphism theorems of linear groups

Genco FASThe goal in this thesis is the isomorphism theory of linear groups over fields as shownby the theoremTheorem: There is an isomorphism between any subset of the (projective) collineartransformations, (projective) general linear groups or (projective) special linear groups fordimension ≥ 3 if and only if the dimensions of the finite dimensional vector spaces of thesesubspaces are equal and the underlying fields of these vector spaces are isomorphic.The theory that follows is typical of much of the research between the years 50?s and60?s on the isomorphisms of the classical groups over rings. The thesis will start from thebasic facts of calculus of residues and transvections. Then, in particular, the fundamentaltheorem of projective geometry will be proved and whatever is needed from projectivegeometry will be developed. Via reorganizing the literature on the isomorphisms of theclassical groups, it will be possible to extend the known theory from groups of lineartransformations to groups of collinear transformations, and also to improve the isomorphismtheory from dimension ≥ 5 to dimension ≥ 3.