Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2015; 52(1): 239-246

Printed January 31, 2015

https://doi.org/10.4134/BKMS.2015.52.1.239

Copyright © The Korean Mathematical Society.

Quasi-commutative semigroups of finite order related to Hamiltonian groups

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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