Expressing group elements as commutators
نویسندگان
چکیده
منابع مشابه
On the Spectra of Group Commutators
1. All operators will be supposed bounded, linear (everywhere defined) over a Hilbert space. By the commutator, C, of two operators A and B will be meant the operator (1) C = AB BA. A conjecture of Kaplansky, cited in [4], that if A commutes with C, so that (2) AC = CA, then (3) sp(C) = 0 only (sp = spectrum), was recently proved by Kleinecke [6] and Shirokov [9]. Earlier proofs of (3) under th...
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we observe that the transform, with respect to any operator of 6r, of the commutators formed with t and the operators of G is the product of two such commutators. All of these commutators must, therefore, form a group which is transformed into itself by G. When t transforms G into itself the given commutators generate the smallest self-conjugate subgroup of G which has the property that all of ...
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We construct quantum commutators on module-algebras of quasitriangular Hopf algebras. These are quantum-group covariant, and have generalized antisymmetry and Leibniz properties. If the Hopf algebra is triangular they additionally satisfy a generalized Jacobi identity, turning the modulealgebra into a quantum-Lie algebra. The purpose of this short communication is to present a quantum commutato...
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We prove that every group G of order n has t,log n/log 2+0dog log n) elements x, x, such that every group element is a product of the form x,'-• X,'% e ; s 1,0, 11. The result is true more generally for quasigroups. As a corollary we obtain that for n even, every one-factorization of the complete graph on n vertices contains at most r one-factors whose union is connected. The aim of this note i...
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Charles Sims has asked whether or not, for a free group F , the lower central subgroup γn(F ) coincides with the normal closure in F of the set of basic commutators of weight n. In this paper, we will show that Sims’ question has a positive answer when n = 5. The longest part of the proof is showing that this is true when F has rank 3. Once this is known, the results for higher ranks follow fai...
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ژورنال
عنوان ژورنال: Rocky Mountain Journal of Mathematics
سال: 1980
ISSN: 0035-7596
DOI: 10.1216/rmj-1980-10-3-651