QUASI-COMMUTATIVE SEMIGROUPS OF FINITE ORDER RELATED TO HAMILTONIAN GROUPS

Abstract

If for every elements x and y of an associative algebraic structure (S, <TEX>${\cdot}$</TEX>) there exists a positive integer r such that <TEX>$ab=b^ra$</TEX>, then S is called quasi-commutative. Evidently, every abelian group or commutative semigroup is quasi-commutative. Also every finite Hamiltonian group that may be considered as a semigroup, is quasi-commutative however, there are quasi-commutative semigroups which are non-group and non commutative. In this paper, we provide three finitely presented non-commutative semigroups which are quasi-commutative. These are the first given concrete examples of finite semigroups of this type.