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Left Ordered Amenable and Locally Indicable Groups
Author(s) -
Linnell Peter A.
Publication year - 1999
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/s0024610799007462
Subject(s) - mathematics , group (periodic table) , combinatorics , locally compact space , amenable group , locally finite group , pure mathematics , physics , abelian group , countable set , quantum mechanics
There has been interest recently concerning when a left ordered group is locally indicable. Chiswell and Kropholler proved that every left ordered solvable‐by‐finite group is locally indicable, while Bergman gave examples of left ordered groups which are not locally indicable. This paper proves that every left ordered elementary amenable group is locally indicable. Every solvable‐by‐finite group is elementary amenable, and every elementary amenable group is amenable. The author leaves it as an open problem as to whether every left ordered amenable group is locally indicable.