Weight Five Basic Commutators as Relators
نویسندگان
چکیده
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 fairly quickly. The authors dedicate this paper to the memory of Hermann V. Waldinger.
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Basic commutators in weights six and seven as relators
Charles Sims has asked whether or not the lower central subgroup γn(F ) of a free group F coincides with the normal closure in F of the basic commutators of weight n. This question has a positive answer in weights at most 5, but remains an open question in general. In earlier work with Gaglione and Spellman, it was shown that γn(F ) is the normal closure in F of the basic commutators of weights...
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