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o-Groups of finite rank and divisibility in their groups of o-automorphisms

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Abstract

We provide a full description of totally ordered groups of finite archimedean rank and study solvability of equations of the form \(x^n=g\) in the group of ordered automorphisms of an a-closed totally ordered group G of finite archimedean rank. We also give a full description of these groups of o-automorphisms and a characterization of the elements of a particular group that have an n-th root.

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Authors and Affiliations

  1. Mathematical Sciences Department, University of South Dakota, Vermillion, SD,  57069, USA

    Ramiro H. Lafuente-Rodriguez

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  1. Ramiro H. Lafuente-Rodriguez
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Correspondence to Ramiro H. Lafuente-Rodriguez.

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Presented by W. Wm. McGovern.

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Lafuente-Rodriguez, R.H. o-Groups of finite rank and divisibility in their groups of o-automorphisms. Algebra Univers. 79, 81 (2018). https://doi.org/10.1007/s00012-018-0563-3

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  • DOI: https://doi.org/10.1007/s00012-018-0563-3

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