21.10 ReduceStabChain

ReduceStabChain( G )

ReduceStabChain removes trivial stabilizers from a known stabilizer chain of the permutation group G. The result is a reduced stabilizer chain (also see ExtendStabChain).

    gap> s4 := Group( (1,2), (1,2,3,4) );;
    gap> Base( s4 );
    [ 1, 2, 3 ]
    gap> ExtendStabChain( s4, [ 1, 2, 3, 4 ] );  Base( s4 );
    [ 1, 2, 3, 4 ]
    gap> PermGroupOps.Indices( s4 );
    [ 4, 3, 2, 1 ]
    gap> ReduceStabChain( s4 );  Base( s4 );
    [ 1, 2, 3 ] 

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