A note on commutators in the group of infinite triangular matrices over a ring
Autor:Bier, Agnieszka ; Hołubowski, Waldemar
Streszczenie: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.
Data wydania: Format: Identyfikator zasobu: Źródło:Linear and Multilinear Algebra 2015 vol. 63, no. 11, s. 2301-2310
Język: Powiązania:Wydział Matematyki Stosowanej. Politechnika Śląska
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