Abstract
Over a commutative ring R with invertible element 2 and with radical ℑ, nets (i.e., tables Б=(Бij) of ideals Бij such that БirБrj ∋ Бij) such that Б ii ∋ℑ are considered. Such nets are called pseudoradical. The groups of the lower central series and the derived series are explicitly constructed for the corresponding net subgroups G (Б) (of the general linear group GL (n,R)) in terms of Б.
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Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 114, pp. 180–186, 1982.
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Roloff, H. Lower central series and derived series of net subgroups of the general linear group. J Math Sci 27, 2968–2974 (1984). https://doi.org/10.1007/BF01410751
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DOI: https://doi.org/10.1007/BF01410751