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abelian algebra assume automorphisms big dilation bijection CC(a CDC(a char F characteristic roots Chevalley groups classical groups Clearly commutator conjugate consider contains contragredient DC(a define denote distinct easily seen element of GLn(V equation F-space field isomorphism fixed hyperplane fixed space follows fractional ideal free module full of projective full of transvections geometric transformation GLn(M group isomorphism group of projectivities hence homomorphism hyperplane H integral domains involutions in PSL2 Isomorphism Theorems linear groups linear transformations mapping Math matrix maximal group module nontrivial projective transvection nontrivial radiation nontrivial transvection nonzero normal subgroup nth roots permute projectively PGLn Pl(V preserves projective collinear transformation Projective Geometry PROOF prove PSLn PTLn residual line residual space roots of unity SLn(M SLn(V spaces L C H subset subspace Suppose transformation g transvection in G transvection with residual transvections with spaces trivial typical unipotent vector space
Page i - ... homotopy theory 6. Walter Rudin: Lectures on the edge-of-the-wedge theorem 7. Yozo Matsushima: Holomorphic vector fields on compact Kahler manifolds 8. Peter Hilton: Lectures in homological algebra 9. IN Herstein: Notes from a ring theory conference 10. Branko Grunbaum: Arrangements and spreads 11. Irving Glicksberg: Recent results on function algebras 12. Barbara L. Osofsky: Homological dimensions of modules 13. Michael Rabin: Automata on infinite objects and Church
Page vii - PSLn(o)2'PSLnl(ol)*=*n = nl and 0 = 0, for dimensions > 3. The theory that follows is typical of much of the research of the last decade on the isomorphisms of the classical groups over rings.
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