GAP:Endomorphisms

This article is about a GAP function.

Definition

Package requirement

This function is part of the SONATA package.

Function type

The function takes as input a group and outputs a list of maps.

Behavior

The function takes as input a group and outputs the endomorphisms from the group to itself as a list.

Related functions

• GAP:Automorphisms returns the set of automorphisms as a list of maps.
• GAP:AutomorphismGroup returns the group of automorphisms.

Examples of usage

gap> Endomorphisms(CyclicGroup(2));
[ [ f1 ] -> [ <identity> of ... ], [ f1 ] -> [ f1 ] ]
gap> Endomorphisms(SymmetricGroup(3));
[ [ (1,2,3), (1,2) ] -> [ (), () ], [ (1,2,3), (1,2) ] -> [ (), (1,3) ], [ (1,2,3), (1,2) ] -> [ (), (2,3) ], [ (1,2,3), (1,2) ] -> [ (), (1,2) ],
  [ (1,2,3), (1,2) ] -> [ (1,2,3), (1,3) ], [ (1,2,3), (1,2) ] -> [ (1,3,2), (1,2) ], [ (1,2,3), (1,2) ] -> [ (1,3,2), (1,3) ],
  [ (1,2,3), (1,2) ] -> [ (1,2,3), (2,3) ], [ (1,2,3), (1,2) ] -> [ (1,2,3), (1,2) ], [ (1,2,3), (1,2) ] -> [ (1,3,2), (2,3) ] ]