Some diophantine problems arising from the theory of cyclically-presented groups

R. W. K. Odoni

doi:10.1017/S0017089599950383

Abstract

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Let n∈ℕ and let Fn be the free group on n generators. Let w be an arbitrary word in Fn, and let σ be an n-cycle in Sn. We consider groups of the type Γ(n,w)=Fn/N, where N is the normal closure in Fn of the “cycled words’’ w, σ(w), σ2(w),…,σn−1(w), and solve, by means of classical algebraic number theory, the following problems.

A. When is Γ(n,w)ab infinite?

B. When is Γ(n,w) a perfect group?

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This article has been cited by the following publications. This list is generated based on data provided by Crossref.

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Some diophantine problems arising from the theory of cyclically-presented groups

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