A1 - Bier, Agnieszka
A1 - Hołubowski, Waldemar
N2 - We investigate the commutators of elements of the group UT(∞,R) of infinite unitriangular matrices over an associative ring R with 1 and a commutative group R* of invertible elements. We prove that every unitriangular matrix of a specified form is a commutator of two other unitriangular matrices. As a direct consequence we give a complete characterization of the lower central series of the group UT(∞,R) including the width of its terms with respect to basic commutators and Engel words. With an additional restriction on the ring R, we show that the derived subgroup of T(∞,R) coincides with the group UT(∞,R). The obtained results generalize the results obtained for triangular groups over a field.
L1 - http://repolis.bg.polsl.pl/Content/31970/BH_Revised.pdf
L2 - http://repolis.bg.polsl.pl/Content/31970
ER -
T1 - A note on commutators in the group of infinite triangular matrices over a ring
UR - http://repolis.bg.polsl.pl/dlibra/docmetadata?id=31970