The Rank of a Direct Power of a Small-Cancellation Group |
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Authors: | Daniel T Wise |
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Institution: | (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 G
n
such that rank((G
n
)n)=2. We conjecture that if G is a word-hyperbolic group then rank(G
n
) as $ n. For each m we give an example of a residually finite
group K
m
such that K
m
has exactly two relators, but K
m
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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