Botto Mura, Roberta; Rhemtulla, Akbar Orderable groups. (English) Zbl 0358.06038 Lecture Notes in Pure and Applied Mathematics. Vol. 27. New York-Basel: Marcel Dekker, Inc. IV, 169 p. SFrs. 66.00 (1977). The first monograph having as main topic the orderability of groups has been written by A. I. Kokorin and V. M. Kopytov [Линейно упорядоченные группы (Russian). Moskva: Nauka (1972; Zbl 0258.06012); English translation: Fully ordered groups. New York-Toronto: John Wiley & Sons (1974)]. The present book contains new material (many of the recent results are due to the authors of the book). From the authors’ introduction: “The point of view we take here is definitely group theoretical. This approach is narrow and does not include many important aspects, such as topological properties, Hahn’s embedding theorem and lattice-ordered groups. Our main interest is in the interplay between orderability properties and group theoretical conditions, such as nilpotency, solvability and finiteness of rank. In particular we have discussed closure properties of several classes related to orderable groups and have included P. Hall’s embedding theorems.” Reviewer: Jan Jakubík (Košice) Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 44 Documents MSC: 06F15 Ordered groups 06-02 Research exposition (monographs, survey articles) pertaining to ordered structures 06F20 Ordered abelian groups, Riesz groups, ordered linear spaces 20-02 Research exposition (monographs, survey articles) pertaining to group theory 20F60 Ordered groups (group-theoretic aspects) Citations:Zbl 0258.06012 PDFBibTeX XML