62.74 SmallestGeneratingSystem

SmallestGeneratingSystem( group )

SmallestGeneratingSystem computes a smallest generating system of the group group i.e. a smallest subset of the elements of the group s.t. the group is generated by this subset.

Remark: there is a GAP standard library function Smallest-Generators for permutation groups. This function computes a generating set of a given group such that its elements are smallest possible permutations (w.r.t. the GAP internal sorting of permutations).

  gap> s5 := SymmetricGroup( 5 );
  Group( (1,5), (2,5), (3,5), (4,5) )
  gap> SmallestGenerators( s5 );
  [ (4,5), (3,4), (2,3), (1,2) ]
  gap> SmallestGeneratingSystem( s5 );
  [ (1,3,5)(2,4), (1,2)(3,4,5) ]

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