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Polycyclic right-ordered groups

Partially Ordered Algebraic Structures

Part of the Lecture Notes in Mathematics book series (LNM,volume 848)

Abstract

A right-ordered group is any subgroup of a group of order preserving permutations of some totally ordered set. It can also be characterized as a group G together with a total order relation ≤ such that a ≤ b implies ac ≤ bc for all a,b,c in G. It is not known whether all such groups G have a series from {e} to G with torsion-free abelian factors. Here we show that a polycyclic right-ordered group must have such a series. This characterizes polycyclic right-ordered groups as the class of poly infinite-cyclic groups.

Keywords

  • Normal Subgroup
  • Polycyclic Group
  • Convex Subgroup
  • Maximal Normal Subgroup
  • Engel Group

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. P. F. Conrad, "Right-ordered groups", Michigan Math. J. 6(1959), 267–275.

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© 1981 Springer-Verlag

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Rhemtulla, A.H. (1981). Polycyclic right-ordered groups. In: Amayo, R.K. (eds) Algebra Carbondale 1980. Lecture Notes in Mathematics, vol 848. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090569

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  • DOI: https://doi.org/10.1007/BFb0090569

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-10573-2

  • Online ISBN: 978-3-540-38549-3

  • eBook Packages: Springer Book Archive