Preserving torsion orders when embedding into groups with `small' finite presentations

Maurice Chiodo; Michael E. Hill

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arXiv · 1610.00977

Preserving torsion orders when embedding into groups with `small' finite presentations

Maurice Chiodo·Michael E. Hill

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Abstract

We give a complete survey of a construction by Boone and Collins for embedding any finitely presented group into one with $8$ generators and $26$ relations. We show that this embedding preserves the set of orders of torsion elements, and in particular torsion-freeness. We combine this with the independent results of Belegradek and Chiodo to prove that there is an $8$-generator $26$-relator universal finitely presented torsion-free group (one into which all finitely presented torsion-free groups embed).

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Maurice Chiodo, Michael E. Hill. 2016-10-04. Preserving torsion orders when embedding into groups with `small' finite presentations. https://arxiv.org/abs/1610.00977

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