On groups with specified lower central series quotients
نویسندگان
چکیده
منابع مشابه
Central Quotients of Biautomatic Groups
The quotient of a biautomatic group by a subgroup of the center is shown to be biautomatic. The main tool used is the Neumann-Shapiro triangulation of S, associated to a biautomatic structure on Zn. As an application, direct factors of biautomatic groups are shown to be biautomatic. Biautomatic groups form a wide class of finitely presented groups with interesting geometric and computational pr...
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In this paper, we first present some properties of lower and upper central series of pair of groups. Then the notion of $n$-isoclinism for the classification of pairs of groups is introduced, and some of the structural properties of the created classes are proved. Moreover some interesting theorems such as Baer Theorem, Bioch Theorem, Hirsh Theorem for pair of groups are generalized...
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This paper examines the behavior of the successive quotients Ni(A) of the lower central series ideals Mi(A) of a nitely generated associative algebra A over Z. We de ne the lower central series Li(A) by L1(A) = A, Li+1(A) = [A,Li(A)], Mi(A) = A · Li(A) · A, and Ni(A) = Mi(A)/Mi+1(A). We decompose the Ni into its free and torsion components using the structure theorem of nitely generated abelian...
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We continue the study of the lower central series and its associated graded components for a free associative algebra with n generators, as initiated in [FS]. We establish a linear bound on the degree of tensor field modules appearing in the Jordan-Hölder series of each graded component, which is conjecturally tight. We also bound the leading coefficient of the Hilbert polynomial of each graded...
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Let A be a noncommutative associative algebra, viewed as a Lie algebra via definition of the Lie bracket [x, y] = xy − yx. Define the lower central series filtration inductively by L1(A) = A, and Li+1(A) = [A,Li(A)]. Denote the components of its associated graded space by Bi(A) = Li(A)/Li+1(A). The components of the associated graded space are well understood in the cases when A = An = the free...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 1978
ISSN: 0030-8730,0030-8730
DOI: 10.2140/pjm.1978.74.83