Some results on saturated numerical semigroups

In this thesis, saturated numerical semigroups which form a subclass of Arf numerical semigroups are discussed. From these saturated numerical semigroups, those with multiplicty less than 9 and given conductor K are considered and some results are obtained. First, some definitions and theorems underlying the numerical semigroups are given. Later, the basic features of Arf numerical semigroups are included. In particular, the structures of Arf numerical semigroups whose multiplicity is less than 9 and whose conductor is known, and some theorems in these semigroups are discussed. Using these Arf numerical semigroups, are given all saturated numerical semigroups with multiplicity is less than 9 and whose conductor is known, and are obtained some theorems and results in these saturated numerical semigroups.