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QUASI-COMMUTATIVE SEMIGROUPS OF FINITE ORDER RELATED TO HAMILTONIAN GROUPS

Sorouhesh, Mohammad Reza;Doostie, Hossein

  • Received : 2013.12.21
  • Published : 2015.01.31

Abstract

If for every elements x and y of an associative algebraic structure (S, ${\cdot}$) there exists a positive integer r such that $ab=b^ra$, 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.

Keywords

quasi-commutativity;finitely presented semigroups

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