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. 2022 Apr;105(3):2011-2045.
doi: 10.1112/jlms.12552. Epub 2022 Feb 16.

Embeddings into left-orderable simple groups

Arman Darbinyan  1 , Markus Steenbock  2
Affiliations

Embeddings into left-orderable simple groups

Arman Darbinyan et al. J Lond Math Soc. 2022 Apr.

Abstract

We prove that every countable left-ordered group embeds into a finitely generated left-ordered simple group. Moreover, if the first group has a computable left-order, then the simple group also has a computable left-order. We also obtain a Boone-Higman-Thompson type theorem for left-orderable groups with recursively enumerable positive cones. These embeddings are Frattini embeddings, and isometric whenever the initial group is finitely generated. Finally, we reprove Thompson's theorem on word problem preserving embeddings into finitely generated simple groups and observe that the embedding is isometric.

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