The cocycle equation on periodic semigroups

Abstract. The cocycle functional equation $$F(x,y) + F(xy, z) = F(x,yz) + F(y,z)$$ has a long and rich history, with important roles in contexts from homological algebra to polyhedral algebra to information theory. This paper deals with the problem of finding explicit forms of symmetric cocycles on periodic semigroups. A semigroup S is periodic if each of its elements has finite order, that is if the cyclic subsemigroup $$\langle a \rangle = \{ …