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||Decidable in polynomial time|
||decidable in polynomial time|
A semigroup is a structure S = (S,·), where · is an infix binary operation, called the
semigroup product, such that
· is associative: (xy)z = x(yz).
Let S and T be semigroups. A morphism from S
to T is a function h : S→T that is a homomorphism:
h(xy) = h(x)h(y).
(XX,o), the collection of functions on a
sets X, with composition.
(Σ + ,·), the collection of nonempty
strings over Σ, with concatenation.
Search for finite semigroups
Size 1: 1
Size 2: 5
Size 3: 24
Size 4: 188
[Size 5]?: 1915
[Size 6]?: 28634
[Size 7]?: 1627672
[Semigroups in the Encyclopedia of Integer Sequences]
Semigroups with zero