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? Thanks in advance, Jonathan _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
