Commutator equations in free groups |
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| Authors: | E Rips |
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| Institution: | (1) Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel |
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| Abstract: | Letf
1, …,f
n be free generators of a free groupF. We consider the equation z
1, …,z
n]ω. where ω and ω′ indicate the disposition of brackets in the higher commutators z
1, …,z
n]ω and f
1, …,f
n]ω. We give a necessary and sufficient condition on ω and ω′ for the existence of solutions of this equation. It is also shown
that for any solutionz
1=r1, …,z
z=r
n we have <r
1, …,r
n>=〈f
1, …f
n〉. |
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| Keywords: | |
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