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# GAP — A Tutorial

Release 4.16.0, 2026-06-02

The GAP Group
Email: support@gap-system.org
Homepage: https://www.gap-system.org

### Copyright

Copyright © (1987-2026) for the core part of the GAP system by the GAP Group.

Most parts of this distribution, including the core part of the GAP system are distributed under the terms of the GNU General Public License, see https://www.gnu.org/licenses/gpl.html or the file `GPL` in the `etc` directory of the GAP installation.

More detailed information about copyright and licenses of parts of this distribution can be found in Reference: Copyright and License.

GAP is developed over a long time and has many authors and contributors. More detailed information can be found in Reference: Authors and Maintainers.

### Contents

1 Preface
1.1 The GAP System
2 A First Session with GAP
2.1 Starting and Leaving GAP
2.2 Loading Source Code from a File
2.3 The Read Evaluate Print Loop
2.4 Constants and Operators
2.5 Variables versus Objects
2.6 Objects vs. Elements
2.7 About Functions
2.8 Help
2.9 Further Information introducing the System
3 Lists and Records
3.1 Plain Lists
3.2 Identical Lists
3.3 Immutability
3.4 Sets
3.5 Ranges
3.6 For and While Loops
3.7 List Operations
3.8 Vectors and Matrices
3.9 Plain Records
3.10 Further Information about Lists
4 Functions
4.1 Writing Functions
4.2 If Statements
4.3 Local Variables
4.4 Recursion
4.5 Further Information about Functions
5 Groups and Homomorphisms
5.1 Permutation groups
5.2 Actions of Groups
5.3 Subgroups as Stabilizers
5.4 Group Homomorphisms by Images
5.5 Nice Monomorphisms
5.6 Further Information about Groups and Homomorphisms
6 Vector Spaces and Algebras
6.1 Vector Spaces
6.2 Algebras
6.3 Further Information about Vector Spaces and Algebras
7 Domains
7.1 Domains as Sets
7.2 Algebraic Structure
7.3 Notions of Generation
7.4 Domain Constructors
7.5 Forming Closures of Domains
7.6 Changing the Structure
7.7 Subdomains
7.8 Further Information about Domains
8 Operations and Methods
8.1 Attributes
8.2 Properties and Filters
8.3 Immediate and True Methods
8.4 Operations and Method Selection
References
Index
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