21.11 MakeStabChainStrongGenerators

MakeStabChainStrongGenerators( G, base, stronggens )

MakeStabChainStrongGenerators computes a reduced stabilizer chain for the permutation group G with the base base and the strong generating set stronggens. stronggens must be a strong generating set for G relative to the base base; note that this is not tested. Since the generators for G are not changed the strong generating set of G got by PermGroupOps.StrongGenerators is not exactly stronggens afterwards. This function is mostly used to reconstruct a stabilizer chain for a group G and works considerably faster than MakeStabChain (see MakeStabChain).

    gap> G := Group( (1,2), (1,2,3), (4,5) );;
    gap> Base( G );
    [ 1, 2, 4 ]
    gap> ExtendStabChain( G, [1,2,3,4] );
    gap> PermGroupOps.Indices( G );  base := Base( G );
    [ 3, 2, 1, 2 ]    # note that the stabilizer chain is not reduced
    [ 1, 2, 3, 4 ]
    gap> stronggens := PermGroupOps.StrongGenerators( G );
    [ (4,5), (2,3), (1,2), (1,2,3) ]
    gap> H := Group( (1,2), (1,3), (4,5) );
    Group( (1,2), (1,3), (4,5) )    # of course <G> = <H>
    gap> MakeStabChainStrongGenerators( H, base, stronggens );
    gap> PermGroupOps.Indices( H );  Base( H );
    [ 3, 2, 2 ]       # note that the stabilizer chain is reduced
    [ 1, 2, 4 ]
    gap> PermGroupOps.StrongGenerators( H );
    [ (4,5), (2,3), (1,2), (1,3) ]
    # note that this is different from 'stronggens' 

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