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<p>We&#xa0;consider torus knot groups that are defined by two generators and a&#xa0;relation between them.Given a&#xa0;pair of coprime integers, we show how to represent such a&#xa0;group as a&#xa0;cyclic extension of a&#xa0;free group.This is achieved by finding a&#xa0;generating set for the free group and finding the required automorphism.The&#xa0;result obtained makes it possible to study automorphisms of such cyclic extensions by studying automorphisms of torus knot groups.</p>

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Structure and Automorphisms of Some Cyclic Extensions of Free Groups

  • 期刊论文

  • 发表日期：

    2026年7月30日

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  • E. A. Shaporina

摘要

We consider torus knot groups that are defined by two generators and a relation between them.Given a pair of coprime integers, we show how to represent such a group as a cyclic extension of a free group.This is achieved by finding a generating set for the free group and finding the required automorphism.The result obtained makes it possible to study automorphisms of such cyclic extensions by studying automorphisms of torus knot groups.