Semigroups

The Semigroups package is a GAP package containing methods for semigroups, monoids, and inverse semigroups, principally of transformations, partial permutations, bipartitions, subsemigroups of regular Rees 0-matrix semigroups, free inverse semigroups, and free bands. Semigroups contains more efficient methods than those available in the GAP library (and in many cases more efficient than any other software) for creating semigroups, monoids, and inverse semigroup, calculating their Green’s structure, ideals, size, elements, group of units, small generating sets, testing membership, finding the inverses of a regular element, factorizing elements over the generators, and many more. It is also possible to test if a semigroup satisfies a particular property, such as if it is regular, simple, inverse, completely regular, and a variety of further properties. There are methods for finding congruences of certain types of semigroups, the normalizer of a semigroup in a permutation group, the maximal subsemigroups of a finite semigroup, and smaller degree partial permutation representations of inverse semigroups. There are functions for producing pictures of the Green’s structure of a semigroup, and for drawing bipartitions.


References in zbMATH (referenced in 32 articles )

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  1. Carvalho, Catarina; Martin, Barnaby: The lattice and semigroup structure of multipermutations (2022)
  2. East, James; Ruškuc, Nik: Classification of congruences of twisted partition monoids (2022)
  3. Dolinka, Igor; Đurđev, Ivana; East, James: Sandwich semigroups in diagram categories (2021)
  4. East, James: Structure of principal one-sided ideals (2021)
  5. East, James; Gray, Robert D.: Ehresmann theory and partition monoids (2021)
  6. East, James: Idempotents and one-sided units: lattice invariants and a semigroup of functors on the category of monoids (2020)
  7. East, James: Transformation representations of sandwich semigroups (2020)
  8. Fleischer, Lukas; Jack, Trevor: The complexity of properties of transformation semigroups (2020)
  9. Dolinka, Igor; East, James; Evangelou, Athanasios; FitzGerald, Des; Ham, Nicholas; Hyde, James; Loughlin, Nicholas; Mitchell, James D.: Enumeration of idempotents in planar diagram monoids (2019)
  10. East, James: Idempotents and one-sided units in infinite partial Brauer monoids (2019)
  11. East, James; Egri-Nagy, Attila; Mitchell, James D.; Péresse, Yann: Computing finite semigroups (2019)
  12. East, James; Gadouleau, Maximilien; Mitchell, James D.: Structural aspects of semigroups based on digraphs (2019)
  13. Feng, Ying-Ying; Al-Aadhami, Asawer; Dolinka, Igor; East, James; Gould, Victoria: Presentations for singular wreath products (2019)
  14. Jonušas, Julius; Troscheit, Sascha: Random ubiquitous transformation semigroups (2019)
  15. Dolinka, Igor; Đurđev, Ivana; East, James; Honyam, Preeyanuch; Sangkhanan, Kritsada; Sanwong, Jintana; Sommanee, Worachead: Sandwich semigroups in locally small categories. II: Transformations (2018)
  16. Dolinka, Igor; East, James: Semigroups of rectangular matrices under a sandwich operation (2018)
  17. Donoven, C. R.; Mitchell, J. D.; Wilson, W. A.: Computing maximal subsemigroups of a finite semigroup (2018)
  18. East, James; Kumar, Jitender; Mitchell, James D.; Wilson, Wilf A.: Maximal subsemigroups of finite transformation and diagram monoids (2018)
  19. East, James; Mitchell, James D.; Ruškuc, Nik; Torpey, Michael: Congruence lattices of finite diagram monoids (2018)
  20. Cameron, P. J.; Castillo-Ramirez, A.; Gadouleau, M.; Mitchell, J. D.: Lengths of words in transformation semigroups generated by digraphs (2017)

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