nLab Wagner-Preston theorem




The Wagner-Preston theorem is a generalization of Cayley's theorem to inverse semigroups. The same idea, when sets have additional local structure, is responsible for the appearance of pseudogroups of symmetries in geometry.


Every inverse semigroup has an injective homomorphism into the inverse semigroup of partial bijections of some set.


  • V. V. Wagner, Generalised groups. Proceedings of the USSR Academy of Sciences (in Russian) 84 (1952), 1119–1122.

  • V. V. Wagner, The theory of generalised heaps and generalised groups, Matematicheskii Sbornik. Novaya Seriya (in Russian). 32 (74) (1953): 545–632.

  • G. B. Preston, Representation of inverse semi-groups, J. London Math. Soc. 29 (1954) 411-419

  • planetmath

  • wikipedia: inverse semigroup

category: algebra

Last revised on September 5, 2023 at 07:37:44. See the history of this page for a list of all contributions to it.