The Rank of a Direct Power of a Small-Cancellation Group |
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Authors: | Daniel T. Wise |
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Affiliation: | (1) Department of Mathematics, Cornell University, Malott Hall, Ithaca, NY, U.S.A. |
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Abstract: | We construct an example of a finitely generated group G such that rank((G)n)=2 for all n1. For each n, we construct a finitely presented group Gn such that rank((Gn)n)=2. We conjecture that if G is a word-hyperbolic group then rank(Gn) as $ n. For each m we give an example of a residually finite group Km such that Km has exactly two relators, but Km has no proper subgroups of index $ m. We construct a finitely generated group D such that there is an epimorphism DD×D. |
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Keywords: | direct sums growth sequence rank residually finite small cancellation theory word-hyperbolic |
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