Notre Dame Journal of Formal Logic 39 (2):157-189 (1998)

Abstract
We study theorems of ordered groups from the perspective of reverse mathematics. We show that suffices to prove Hölder's Theorem and give equivalences of both (the orderability of torsion free nilpotent groups and direct products, the classical semigroup conditions for orderability) and (the existence of induced partial orders in quotient groups, the existence of the center, and the existence of the strong divisible closure)
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DOI 10.1305/ndjfl/1039293061
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Ordered Groups: A Case Study in Reverse Mathematics.Reed Solomon - 1999 - Bulletin of Symbolic Logic 5 (1):45-58.
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The Complexity of Central Series in Nilpotent Computable Groups.Barbara F. Csima & Reed Solomon - 2011 - Annals of Pure and Applied Logic 162 (8):667-678.

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