62.44 Subnearrings

Subnearrings( nr )

The function Subnearrings computes all subnear-rings of the near-ring nr. The function returns a list of near-rings representing the according subnear-rings. In case that nr is a transformation near-ring, FindGroup is used to determine the additive group of nr as a permutation group.

  gap> Subnearrings( LibraryNearring( "V4", 22 ) );
  [ Nearring( Subgroup( V4, [  ] ), function ( x, y )
          return elms[tfle.(f[Position( elms, y )])[Position( elms, x )]
             ];
      end ), Nearring( Subgroup( V4, [ (3,4) ] ), function ( x, y )
          return elms[tfle.(f[Position( elms, y )])[Position( elms, x )]
             ];
      end ), Nearring( Subgroup( V4, [ (1,2) ] ), function ( x, y )
          return elms[tfle.(f[Position( elms, y )])[Position( elms, x )]
             ];
      end ), Nearring( V4, function ( x, y )
          return elms[tfle.(f[Position( elms, y )])[Position( elms, x )]
             ];
      end ) ]

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