62.73 InnerAutomorphisms

InnerAutomorphisms( group )

InnerAutomorphisms computes all the inner automorphisms of the group group. The inner automorphisms are returned as a list of transformations s.t. the identity automorphism is always the last entry in this list. For each transformation in this list the record components is-Inner-Auto-mor-phism, is-Group-En-do-mor-phism, and is-Group-Auto-mor-phism are all set to true.

  gap> i := InnerAutomorphisms( d8 );
  [ Transformation( Group( (1,2,3,4), (2,4) ), [ 1, 2, 8, 7, 5, 6, 4, 3 
       ] ), Transformation( Group( (1,2,3,4), (2,4) ), 
      [ 1, 5, 3, 7, 2, 6, 4, 8 ] ), Transformation( Group( (1,2,3,4), 
      (2,4) ), [ 1, 5, 8, 4, 2, 6, 7, 3 ] ), 
    Transformation( Group( (1,2,3,4), (2,4) ), [ 1, 2, 3, 4, 5, 6, 7, 8 
       ] ) ]

Previous Up Top Next
Index