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http://dx.doi.org/10.4134/BKMS.2013.50.3.801

A CONSTRUCTION OF COMMUTATIVE NILPOTENT SEMIGROUPS

Liu, Qiong (Department of Mathematics Shanghai University of Electric Power)
Wu, Tongsuo (Department of Mathematics Shanghai Jiaotong University)
Ye, Meng (Department of Mathematics Shanghai Jiaotong University)

Publication Information

Bulletin of the Korean Mathematical Society / v.50, no.3, 2013 , pp. 801-809 More about this Journal

Abstract

In this paper, we construct nilpotent semigroups S such that $S^n=\{0\}$ , $S^{n-1}{\neq}\{0\}$ and ${\Gamma}(S)$ 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 $n{\geq}5$ . 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;

Citations & Related Records

Reference

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