62.41 FindGroup

FindGroup( nr )

For a transformation near-ring nr, this function computes the additive group of nr as a GAP permutation group and stores it in the record component nr.group.

  gap> t := Transformation( Group( (1,2) ), [2,1] );
  Transformation( Group( (1,2) ), [ 2, 1 ] )
  gap> n := Nearring( t );                          
  Nearring( Transformation( Group( (1,2) ), [ 2, 1 ] ) ) 
  gap> g := FindGroup( n );                         
  Group( (1,2)(3,4), (1,3)(2,4) )
  gap> Elements( g );
  [ (), (1,2)(3,4), (1,3)(2,4), (1,4)(2,3) ]
  gap> Elements( n );
  [ Transformation( Group( (1,2) ), [ 1, 1 ] ), 
    Transformation( Group( (1,2) ), [ 1, 2 ] ), 
    Transformation( Group( (1,2) ), [ 2, 1 ] ), 
    Transformation( Group( (1,2) ), [ 2, 2 ] ) ]

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