Premium
Extensions of Right Orders in Solvable Groups
Author(s) -
Pierce Keith R.
Publication year - 1975
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-11.1.81
Subject(s) - mathematics , order (exchange) , group (periodic table) , nilpotent group , nilpotent , abelian group , p group , combinatorics , pure mathematics , solvable group , cyclic group , non abelian group , algebra over a field , physics , finance , quantum mechanics , economics
We characterize those groups which are extensions of an abelian group by a cyclic group, in which every right order of every subgroup can be extended to a right order of the entire group. Examples are given which illustrate relationships between these groups and v ‐groups (groups in which every 2‐sided total order of every subgroup extends to a 2‐sided order of the entire group). An example is given of a non‐locally‐nilpotent group in which every right partial order extends to a right order.