A construction of commutative nilpotent semigroups
Bull. Korean Math. Soc. 2013 Vol. 50, No. 3, 801-809
Printed May 31, 2013
Qiong Liu, Tongsuo Wu, and Meng Ye
Shanghai University of Electric Power, Shanghai Jiaotong University, Shanghai Jiaotong University
Abstract : In this paper, we construct nilpotent semigroups $S$ such that $S^n=\{0\}$, $S^{n-1}\not=\{0\}$ and $\G(S)$ is a refinement of the star graph $K_{1,n-3}$ with center $c$ together with finitely many or infinitely many end vertices adjacent to $c$, for each finite positive integer $n\ge 5$. We also give counting formulae to calculate the number of the mutually non-isomorphic nilpotent semigroups when $n=5,\, 6$ and in finite cases.
Keywords : nilpotent semigroup, refinement of a star graph, structure, counting formula
MSC numbers : Primary 20M14; Secondary 05C90
Downloads: Full-text PDF  

Copyright © Korean Mathematical Society. All Rights Reserved.
The Korea Science Technology Center (Rm. 411), 22, Teheran-ro 7-gil, Gangnam-gu, Seoul 06130, Korea
Tel: 82-2-565-0361  | Fax: 82-2-565-0364  | E-mail: paper@kms.or.kr   | Powered by INFOrang Co., Ltd