Groups with a positive law on commutators |
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Authors: | David M. Riley Pavel Shumyatsky |
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Affiliation: | a Department of Mathematics, University of Western Ontario, London, Ontario N6A 5B7, Canada b Department of Mathematics, University of Brasilia, 70.910 Brasília, DF, Brazil |
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Abstract: | Let p be a prime number and let G be a finitely generated group that is residually a finite p-group. We prove that if G satisfies a positive law on all elements of the form [a,b][c,d]i, a,b,c,d∈G and i?0, then the entire derived subgroup G′ satisfies a positive law. In fact, G′ is an extension of a nilpotent group by a locally finite group of finite exponent. |
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Keywords: | Primary: 20F50 secondary: 20E10, 20E26, 20F40 |
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