62.31 IsNrMultiplication

IsNrMultiplication( G, mul )

The arguments of the function Is-Nr-Mul-ti-pli-ca-tion are a permutation group G and a GAP function mul which has two arguments x and y which must both be elements of the group G and returns an element z of G s.t. mul defines a binary operation on G.

IsNrMultiplication returns true (false) if mul is (is not) a near-ring multiplication on G i.e. it checks whether it is well-defined, associative and right distributive over the group operation of G.

  gap> g := Group( (1,2), (1,2,3) );        
  Group( (1,2), (1,2,3) )
  gap> mul_r := function(x,y) return x; end;
  function ( x, y ) ... end
  gap> IsNrMultiplication( g, mul_r );
  true
  gap> mul_l := function(x,y) return y; end;
  function ( x, y ) ... end
  gap> IsNrMultiplication( g, mul_l );      
  specified multiplication is not right distributive.
  false

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