Quasi-commutative semigroups of finite order related to Hamiltonian groups
Bull. Korean Math. Soc. 2015 Vol. 52, No. 1, 239-246
https://doi.org/10.4134/BKMS.2015.52.1.239
Printed January 31, 2015
Mohammad Reza Sorouhesh and Hossein Doostie
Tehran Science and Research Branch Islamic Azad University, Tehran Science and Research Branch Islamic Azad University
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
MSC numbers : 20M05
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