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'
GAP 3.4.4