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Inverse semigroups. The theory of partial symmetries. (English) Zbl 1079.20505
Singapore: World Scientific (ISBN 981-02-3316-7). xiv, 411 p. (1998).
Publisher’s description: Symmetry is one of the most important organising principles in the natural sciences. The mathematical theory of symmetry has long been associated with group theory, but it is a basic premise of this book that there are aspects of symmetry which are more faithfully represented by a generalization of groups called inverse semigroups. The theory of inverse semigroups is described from its origins in the foundations of differential geometry through to its most recent applications in combinatorial group theory, and the theory tilings.

20M18 Inverse semigroups
20-02 Research exposition (monographs, survey articles) pertaining to group theory
18B40 Groupoids, semigroupoids, semigroups, groups (viewed as categories)