Basic Commutators in Weights Six and Seven as Relators |
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Authors: | David A Jackson |
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Institution: | 1. Department of Mathematics and Computer Science , Saint Louis University , St. Louis, Missouri, USA jacksoda@slu.edu |
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Abstract: | Charles Sims has asked whether or not the lower central subgroup γ n (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 γ n (F) is the normal closure in F of the basic commutators of weights n through 2n ? 4. Here, we specialize to the case where F has rank 2 and show that γ6(F) is the normal closure in F of the basic commutators of weights 6 and 7. |
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Keywords: | Basic commutator Free group |
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