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.”

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)

##### 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) |