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Commutator Length of Finitely Generated Linear Groups
Author
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2008, Issue 2008 (31 Dec. 2008), pp.1-5, 5 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2008-06-25
Country of Publication
Egypt
No. of Pages
5
Main Subjects
Abstract EN
The commutator length “cl(G)” of a group G is the least natural number c such that every element of the derived subgroup of G is a product of c commutators.
We give an upper bound for cl(G) when G is a d-generator nilpotent-by-abelian-by-finite group.
Then, we give an upper bound for the commutator length of a soluble-by-finite linear group over C that depends only on d and the degree of linearity.
For such a group G, we prove that cl(G) is less than k(k+1)/2+12d3+o(d2), where k is the minimum number of generators of (upper) triangular subgroup of G and o(d2) is a quadratic polynomial in d.
Finally we show that if G is a soluble-by-finite group of Prüffer rank r then cl(G)≤r(r+1)/2+12r3+o(r2), where o(r2) is a quadratic polynomial in r.
American Psychological Association (APA)
Alizadeh Sanati, Mahboubeh. 2008. Commutator Length of Finitely Generated Linear Groups. International Journal of Mathematics and Mathematical Sciences،Vol. 2008, no. 2008, pp.1-5.
https://search.emarefa.net/detail/BIM-987881
Modern Language Association (MLA)
Alizadeh Sanati, Mahboubeh. Commutator Length of Finitely Generated Linear Groups. International Journal of Mathematics and Mathematical Sciences No. 2008 (2008), pp.1-5.
https://search.emarefa.net/detail/BIM-987881
American Medical Association (AMA)
Alizadeh Sanati, Mahboubeh. Commutator Length of Finitely Generated Linear Groups. International Journal of Mathematics and Mathematical Sciences. 2008. Vol. 2008, no. 2008, pp.1-5.
https://search.emarefa.net/detail/BIM-987881
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-987881