Groups with right-invariant multiorders

zbMATH Open1291.06007arXiv1209.3220MaRDI QIDQ2848735

P. J. Cameron

Publication date: 26 September 2013

Published in: The Australasian Journal of Combinatorics (Search for Journal in Brave)

Abstract: A Cayley object for a group G is a structure on which G acts regularly as a group of automorphisms. The main theorem asserts that a necessary and sufficient condition for the free abelian group G of rank m to have the generic n-tuple of linear orders as a Cayley object is that m>n. The background to this theorem is discussed. The proof uses Kronecker's Theorem on diophantine approximation.

Full work available at URL: https://arxiv.org/abs/1209.3220

Mathematics Subject Classification ID

Finite automorphism groups of algebraic, geometric, or combinatorial structures (20B25) Ordered abelian groups, Riesz groups, ordered linear spaces (06F20) Torsion-free groups, finite rank (20K15)

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