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