TY - JOUR
AU - Segal, Daniel
AB - UNIPOTENT GROUPS OF MODULE AUTOMORPHISMS OVER POLYCYCLIC GROUP RINGS DANIEL SEGALt An automorphism y of a module M is called unipotent if y — 1 is a nilpotent endomorphism of M. A group of automorphisms is unipotent if each element of it is unipotent. A group F of automorphisms of M is called stable if F stabilizes a finite series of submodules running from M to 0; equivalently, the image in End(M) of the augmentation ideal of F is a nilpotent ring. The stability length of F is then the length of a shortest series stabilized by F. It is classical that a unipotent group of linear transformations of a finite-dimen- sional vector space M over a field is necessarily stable, and this easily generalizes to the case where M is a finitely generated module over any commutative Noetherian ring (Wehrfritz [7], Chapter 13). Little however seems to be known about the analogous question for modules over noncommutative rings; it is apparently unknown even whether a unipotent group of linear transformations of a finite-dimensional vector space over a skewfield need be stable. Here we settle the question for a special but interesting class of rings, namely group rings of 
TI - Unipotent Groups of Module Automorphisms over Polycyclic Group Rings
JO - Bulletin of the London Mathematical Society
DO - 10.1112/blms/8.2.174
DA - 1976-07-01
UR - https://www.deepdyve.com/lp/wiley/unipotent-groups-of-module-automorphisms-over-polycyclic-group-rings-3yFdXAtdW5
SP - 174
EP - 178
VL - 8
IS - 2
DP - DeepDyve
ER -