Lectures on linear groups. Regional Conference Series in Mathematics 22; Regional conference series in mathematics 22.

O'Meara, O. Timothy:

ISBN 10: 0821816721 / ISBN 13: 9780821816721

Published by Providence, American Mathematical Society, 1974

About this Item

Ex-library with stamp and library-signature. GOOD condition, some traces of use. Ancien Exemplaire de bibliothèque avec signature et cachet. BON état, quelques traces d'usure. Ehem. Bibliotheksexemplar mit Signatur und Stempel. GUTER Zustand, ein paar Gebrauchsspuren. 20 OME 9780821816721 Sprache: Englisch Gewicht in Gramm: 550.

Seller Inventory # 2499202

Bibliographic Details

• Title: Lectures on linear groups. Regional Conference Series in Mathematics 22; Regional conference series in mathematics 22.
• Publisher: Providence, American Mathematical Society
• Publication Date: 1974
• Language: English
• ISBN 10: 0821816721
• ISBN 13: 9780821816721
• Binding: Softcover
• Weight: 550 grams
• Seller catalogs:
  • SA MATHEMATIK

About this title

Synopsis

The notes in this volume evolved from lectures at the California Institute of Technology during the spring of 1968, from ten survey lectures on classical and Chevalley groups at an NSF Regional Conference at Arizona State University in March 1973, and from lectures on linear groups at the University of Notre Dame in the fall of 1973. The author's goal in these expository lectures was to explain the isomorphism theory of linear groups over integral domains as illustrated by the theorem $\mathrm{PSL}_n({\mathfrak o})\simeq\mathrm{PSL}_{n_1}({\mathfrak o}_1)\leftrightarrow n=n_1\quad\mathrm{and}\quad{\mathfrak o}\simeq{\mathfrak o}_1$ for dimensions $geqq 3$. The theory that follows is typical of much of the research of the last decade on the isomorphisms of the classical groups over rings. The author starts from scratch, assuming only basic facts from a first course in algebra. The classical theorem on the simplicity of $\mathrm{PSL}_n(F)$ is proved, and whatever is needed from projective geometry is developed. Since the primary interest is in integral domains, the treatment is commutative throughout. In reorganizing the literature for these lectures the author extends the known theory from groups of linear transformations to groups of collinear transformations, and also improves the isomorphism theory from dimensions $geqq 3$.