ORDERED GROUPS IN WHICH ALL CONVEX JUMPS ARE CENTRAL | Zendy

V. V. Bludov | Zendy; A. M. W. Glass | Zendy; A. H. Rhemtulla | Zendy

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ORDERED GROUPS IN WHICH ALL CONVEX JUMPS ARE CENTRAL

Author(s) -

V. V. Bludov,

A. M. W. Glass,

A. H. Rhemtulla

Publication year - 2003

Publication title -

journal of the korean mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.403

H-Index - 31

eISSN - 2234-3008

pISSN - 0304-9914

DOI - 10.4134/jkms.2003.40.2.225

Subject(s) - mathematics , combinatorics , generator (circuit theory) , nilpotent , regular polygon , nilpotent group , order (exchange) , group (periodic table) , central series , geometry , power (physics) , chemistry , physics , organic chemistry , finance , quantum mechanics , economics

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 2 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 f 1gf g2 for all f;g 2 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.

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