Abstract:
Let $\mathcal{K}$ be a class of semigroups and $\mathcal{P}$ be a set of general properties of semigroups. We call a subset $Q$ of $\mathcal{P}$ characteristic for a semigroup $S\in\mathcal{K}$ if, up to isomorphism and anti-isomorphism, $S$ is the only semigroup in $\mathcal{K}$, which satisfies all the properties from $Q$.
The set of properties $\mathcal{P}$ is called char-complete for $\mathcal{K}$ if for any $S\in \mathcal{K}$
the set of all properties $P\in\mathcal{P}$, which hold for the semigroup $S$, is characteristic for $S$. We indicate a 7-element set of properties of semigroups which is a minimal char-complete set for the class of semigroups of order $3$.
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