Symplectic groups / by O.T. O'Meara.

Format:

Book

Author/Creator:

O'Meara, O. T. (Onorato Timothy), 1928- author.

Series:

Mathematical surveys ; number 16.

Mathematical surveys ; number 16

Language:

English

Subjects (All):

Symplectic groups.

Isomorphisms (Mathematics).

Physical Description:

1 online resource (136 p.)

Edition:

Reprinted with corrections.

Place of Publication:

Providence : American Mathematical Society, 1982.

Language Note:

English

Summary:

Sequel to the author's Lectures on Linear Groups, this book describes isomorphism theory of symplectic groups over integral domains. It presents the description of the isomorphisms of the symplectic groups and their congruence subgroups over integral domains.

Contents:

""Contents""; ""Preface""; ""Prerequisites and Notation""; ""Chapter 1. Introduction""; ""1.1. Alternating Spaces""; ""1.2. Projective Transformations""; ""1.3. Residues""; ""1.4. Transvections""; ""1.5. Matrices""; ""1.6. Projective Transvections""; ""1.7. Some Theorems about SL[sub(n)]""; ""1.8. Comments""; ""Chapter 2. Generation Theorems""; ""2.1. Generation by Transvections in Sp[sub(n)]""; ""2.2. Elementary Generation of Sp[sub(n)]""; ""2.3. Comments""; ""Chapter 3. Structure Theorems""; ""3.1. Orders of Symplectic Groups""; ""3.2. Centers""; ""3.3. Commutator Subgroups""

""3.4. Simplicity Theorems""""3.5. Comments""; ""Chapter 4. Symplectic Collinear Transformations""; ""4.1. Collinear Transformations""; ""4.2. Symplectic Collinear Transformations""; ""4.3. Hyperbolic Transformations""; ""Chapter 5. The Isomorphisms of Symplectic Groups""; ""5.1. Groups with Enough Projective Transvections""; ""5.2. Preservation of Projective Transvections""; ""5.3. The Isomorphism Theorems in General""; ""5.4. 4-Dimensional Groups in Characteristic 2""; ""5.5. Bounded Modules over Integral Domains""; ""5.6. The Isomorphism Theorems over Integral Domains""; ""5.7. Comments""

""Chapter 6. The Nonisomorphisms between Linear and Symplectic Groups""""6.1. The Nonisomorphisms""; ""Index""; ""A""; ""B""; ""C""; ""D""; ""E""; ""F""; ""G""; ""H""; ""I""; ""L""; ""M""; ""N""; ""O""; ""P""; ""R""; ""S""; ""T""; ""U""; ""V""; ""W""

Notes:

Based on lectures given at the University of Notre Dame, 1974-75.

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (ebrary, viewed May 23, 2014).

ISBN:

1-4704-1243-8