This series is refined by the composition series corresponding to the ag system. Analogously you can see whether the group is even elementary abelian. Furthermore the set of public Sylow subgroups forms a Sylow system. You get a smaller generating set of the group by taking only the elements which correspond to local heads of the group. The collection with a special ag system may be faster than the collection with an arbitrary ag system, since in the calculation of the public subgroups of G the commutators of the ag generators are shortened.
Many algorithms are faster for special ag groups than for arbitrary ag groups.
The function SpecialAgGroup takes an ag group G as input and calculates a special ag group H , which is isomorphic to G . Special Ag Group Records . With this options the algorithm takes less time. It calculates an ag group H , which is isomorphic to G . But be careful, because the output H is not handled as a special ag group by GAP but as an arbitrary ag Ag Group Functions for Special Ag Groups use the algorithms for special ag groups.