GAP (recog) - Chapter 1: Introduction

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1 Introduction
1.1 Philosophy
1.2 Overview over this manual
1.3 Feedback and support
1.4 Literature (temporary)

### 1 Introduction

#### 1.1 Philosophy

This package is about group recognition. It provides a generic framework to implement methods of group recognition, regardless of what computational representation is used. This means, that the code in this package is useful at least for permutation groups, and matrix groups and projective groups over finite fields. The setup is described in [NS06].

The framework allows to build composition trees and handles the builtup and usage of these trees in a generic way. It also contains a method selection (described in Chapter 4) that allows to install recognition methods in a convenient way and that automatically tries to try the different available methods in a sensible order.

#### 1.2 Overview over this manual

Chapter 2 describes the installation of this package.

Chapter 3 describes the generic, recursive procedure used for group recognition throughout this package. At the heart of this procedure is the definition of "FindHomomorphism" methods, which is also described in that chapter. For the choice of the right method for finding a homomorphism (or an isomorphism) we use another generic procedure, the "method selection" which is not to be confused with the GAP method selection.

Our own method selection system is described in detail in Chapter 4, because it is interesting in its own right and might be useful in other circumstances.

Chapter 6 describes the available "FindHomomorphism" methods.

Chapter 5 explains what one can do with a completed recognition tree.

Finally, Chapter 7 shows some instructive examples of the usage of this package.

#### 1.3 Feedback and support

If you have any bug reports, feature requests, or suggestions, then please tell us via the issue tracker on GitHub.

In addition, the recog package has a mailing list, at recog@gap-system.org, which can be used for holding discussions, sharing information, and asking questions about the package. You can find more information, and register to receive the mail sent to this list, at https://mail.gap-system.org/mailman/listinfo/recog.

#### 1.4 Literature (temporary)

TODO Find the appropriate place to put these references, so that they appear in the bibliography: [LNPS06] [BLS97] [JLNP13] [DLGLO13] [LGO09] [BLGN+05] [BLGN+03] [NP98] [NP99] [NP97] [Pra99] [CLG97a] [CLG97b] [CLGM+95] [BNS06] [CNRD09] [BHLGO15] [Neu09] [Ser03] [KK15] [LO16] [LO07] [HLO+08] [BB99] [BBS09] [BS01] [Bro01] [Bro08] [Bro03] [BK06] [BK01] [CLG98] [CLGO06] [CLG01] [CFL97] [DLGO15] [GH97] [GLGO06] [HLGOR96a] [HLGOR96b] [HR94] [IL00] [KM13] [KM15] [LGO97a] [LGO02] [LGO97b] [LG01] [LMO07] [NP92] [Nie05] [O'B11] [O'B06] [Pak00] [Par84]

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