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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On ordered polycyclic groups


Author: R. J. Hursey
Journal: Proc. Amer. Math. Soc. 28 (1971), 391-394
MSC: Primary 06.75
MathSciNet review: 0279015
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Abstract: It has been asserted that any (full) order on a torsion-free, finitely generated, nilpotent group is defined by some $ F$-basis of $ G$ and that the group of $ o$-automorphisms of such a group is itself a group of the same kind. Examples provided herein demonstrate that both of these assertions are false; however, it is proved that the group of $ o$-automorphisms of an ordered, polycyclic group is nilpotent by abelian, and polycyclic.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1971-0279015-4
PII: S 0002-9939(1971)0279015-4
Keywords: Polycyclic group, nilpotent group, cyclic normal series, $ F$-series, $ F$-basis, length of a polycyclic group
Article copyright: © Copyright 1971 American Mathematical Society