62.71 Endomorphisms for groups

Endomorphisms( group )

Endomorphisms computes all the endomorphisms of the group group. This function is most essential for computing the near-rings on a group. The endomorphisms are returned as a list of transformations s.t. the identity endomorphism is always the last entry in this list. For each transformation in this list the record component is-Group-En-do-mor-phism is set to true and if such a transformation is in fact an automorphism then in addition the record component is-Group-Auto-mor-phism is set to true.

  gap> g := Group( (1,2,3) );                                         
  Group( (1,2,3) )
  gap> Endomorphisms( g );
  [ Transformation( Group( (1,2,3) ), [ 1, 1, 1 ] ), 
    Transformation( Group( (1,2,3) ), [ 1, 3, 2 ] ), 
    Transformation( Group( (1,2,3) ), [ 1, 2, 3 ] ) ]

Previous Up Top Next
Index