## Lectures on Linear Groups, Issue 22 |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

2 | |

GENERATION THEOREMS | 14 |

STRUCTURE THEORY | 20 |

COLLINEAR TRANSFORMATIONS AND PROJECTIVE GEOMETRY | 28 |

THE ISOMORPHISMS OF LINEAR GROUPS | 40 |

### Common terms and phrases

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

### Popular passages

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 - I found it possible to extend the known theory from groups of linear transformations to groups of collinear transformations, and also to improve the isomorphism theory from dimensions > 5 to dimensions > 3.

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.

Page i - Differential games 19. Bêla Sz.-Nagy: Unitary dilations of Hubert space operators and related topics 20.