A CONSTRUCTION OF COMMUTATIVE NILPOTENT SEMIGROUPS

Title & Authors
A CONSTRUCTION OF COMMUTATIVE NILPOTENT SEMIGROUPS
Liu, Qiong; Wu, Tongsuo; Ye, Meng;

Abstract
In this paper, we construct nilpotent semigroups S such that $\small{S^n=\{0\}}$, $\small{S^{n-1}{\neq}\{0\}}$ and $\small{{\Gamma}(S)}$ is a refinement of the star graph $\small{K_{1,n-3}}$ with center $\small{c}$ together with finitely many or infinitely many end vertices adjacent to $\small{c}$, for each finite positive integer $\small{n{\geq}5}$. We also give counting formulae to calculate the number of the mutually non-isomorphic nilpotent semigroups when $\small{n=5}$, 6 and in finite cases.
Keywords
nilpotent semigroup;refinement of a star graph;structure;counting formula;
Language
English
Cited by
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