This paper has made some discussions on the finite commutative semigroup. The relationship between the finite commutative semigroup and the finite commutativegroup is established.
对有限可换半群进行了讨论，建立了有限可换半群与有限可换群之间的关系。
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First, we give the definition of Lie color superalgebras using the symmetric bicharacter on a finite commutativegroup, and also we introduce some fundamental notions about Lie color superalgebras.
The braid group is infinite non-commutativegroup, and it has many hard problems that can be utilized to design cryptographic primitives, such as the word problem, conjugacy problem and root problem.