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ORDERED GROUPS IN WHICH ALL CONVEX JUMPS ARE CENTRAL
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 Title & Authors
ORDERED GROUPS IN WHICH ALL CONVEX JUMPS ARE CENTRAL
Bludov, V.V.; Glass, A.M.W.; Rhemtulla, Akbar H.;
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 Abstract
(G, <) is an ordered group if'<'is a total order relation on G in which f < g implies that xfy < xgy for all f, g, x, y G. We say that (G, <) is centrally ordered if (G, <) is ordered and [G,D] C for every convex jump C D in G. Equivalently, if for all f, g G with g > 1. Every order on a torsion-free locally nilpotent group is central. We prove that if every order on every two-generator subgroup of a locally soluble orderable group G is central, then G is locally nilpotent. We also provide an example of a non-nilpotent two-generator metabelian orderable group in which all orders are central.
 Keywords
soluble group;locally nilpotent group;ordered group;convex jump;central series;weakly Abelian;
 Language
English
 Cited by
1.
On centrally orderable groups, Journal of Algebra, 2005, 291, 1, 129  crossref(new windwow)
2.
On SolvableR* Groups of Finite Rank, Communications in Algebra, 2003, 31, 7, 3287  crossref(new windwow)
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