On a family of cyclically-presented fundamental groups (Q2765555)
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scientific article; zbMATH DE number 1694850
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On a family of cyclically-presented fundamental groups |
scientific article; zbMATH DE number 1694850 |
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On a family of cyclically-presented fundamental groups (English)
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12 August 2002
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cyclically presented groups
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minimal numbers of generators
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fundamental groups
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\textit{D. L. Johnson, A. C. Kim} and \textit{E. A. O'Brien} [Commun. Algebra 27, No. 7, 3531-3536 (1999; Zbl 0932.20034)] studied two families of cyclically presented groups (depending on an integer \(n\) and having the Alexander polynomials of the knots \(5_2\) and \(6_1\) in the tables), and they suggested that the groups might be generated by two elements. In the present paper, making significant use of computer packages in group theory, upper and lower bounds for the minimal number of generators of these groups are obtained which grow linearly with \(n\). The lower bounds are obtained by considering quotients of the groups which are direct products of alternating groups of degree five.
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