Search results for "generalised kernels"

A reduction theorem for the generalised Rhodes' Type II Conjecture

2018

One of the milestones in the theory of semigroups and automata is the Krohn-Rhodes Theorem. It states that every finite semigroup S divides a wreath product of finite simple groups, each of them divisor of S, and finite aperiodic semigroups, i. e. semigroups with trivial maximal subgroups. The smallest number of groups in any Kohn-Rhodes decomposition is called the group complexity of the semigroup. Since there is no obvious way to compute the complexity of a finite semigroup in general, the decidability of this number is one of the most important open problems in finite semigroup theory and the search for the solution has led to the development of many tools and ideas that are useful in fi…