On the relation between upper central quotients and lower central series of a group
نویسندگان
چکیده
منابع مشابه
Some Structural Properties of Upper and Lower Central Series of Pairs of Groups
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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15 صفحه اولOn the Lower Central Series Quotients of a Graded Associative Algebra
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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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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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2001
ISSN: 0002-9947,1088-6850
DOI: 10.1090/s0002-9947-01-02812-4