Dear Jonathan, > On 19 Dec 2016, at 02:55, Jonathan Gryak <gry...@gmail.com> wrote: > > Hello Forum Members, > The GAP package Polycyclic contains the function MaximalOrderByUnitsPcpGroup > <http://www.gap-system.org/Manuals/pkg/polycyclic-2.11/doc/chap6_mj.html#X78CEF1F27ED8D7BB> > that constructs a polycyclic group that is infinite and non-virtually > nilpotent. These groups are of the form O(F) \rtimes U(F), where F is an > algebraic number field and O(F) and U(F) are respectively the maximal order > and unit group of F, as discussed in the chapter on polycyclic group > in the Handbook > of Computational Group Theory > <https://www.crcpress.com/Handbook-of-Computational-Group-Theory/Holt-Eick-OBrien/p/book/9781584883722> > . > > Is there another method for constructing infinite, non-nilpotent polycyclic > groups that doesn't rely on the split extension method above? And can this > method be implemented in GAP, say via a finite presentation?
This is the primary purpose of the Polycyclic package you already are using: It allows you to work with arbitrary Polycyclic groups. You can do so either by constructing a suitable collector directly (as described in Chapter 3 of the Polycyclic manual), or else by defining a suitable finitely presented group, then using the function IsomorphismPcpGroupFromFpGroupWithPcPres (see chapter 5 of the Polycyclic manual). Regards, Max _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
