25.2 Construction of Ag Groups

The most fundamental way to construct a new finite polycyclic group is AgGroupFpGroup (see AgGroupFpGroup) together with RefinedAgSeries (see RefinedAgSeries), if a presentation for an AG system of a finite polycyclic group is known.

But usually new finite polycyclic groups are constructed from already existing finite polycyclic groups. The direct product of known ag groups can be formed by DirectProduct (see DirectProduct); also, if for instance a permutation representation P of a finite polycyclic group G is known, WreathProduct (see WreathProduct) returns the P-wreath product of G with a second ag group. If a homomorphism of a finite polycyclic group G into the automorphism group of another finite polycyclic group H is known, SemidirectProduct returns the semi direct product of G with H.

Fundamental finite polycyclic groups, such as elementary abelian, arbitrary finite abelian groups, and cyclic groups, are constructed by the appropriate functions (see The Basic Groups Library).

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