The complexity of central series in nilpotent computable groups

The terms of the upper and lower central series of a nilpotent computable group have computably enumerable Turing degree. We show that the Turing degrees of these terms are independent even when restricted to groups which admit computable orders.

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Bibliographic Details
Published in:Annals of pure and applied logic 2011-08, Vol.162 (8), p.667-678
Main Authors: Csima, Barbara F., Solomon, Reed
Format: Article
Language:English
Subjects:
Computable groups
Nilpotent groups
Word problems
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Description
Summary:The terms of the upper and lower central series of a nilpotent computable group have computably enumerable Turing degree. We show that the Turing degrees of these terms are independent even when restricted to groups which admit computable orders.
ISSN:0168-0072
DOI:10.1016/j.apal.2011.01.011