On the Cayley semigroup of a finite aperiodic semigroup

Details On the Cayley semigroup of a finite aperiodic semigroup On the Cayley semigroup of a finite aperiodic semigroup

2008-08-25

arxiv.org/abs/0808.3415v1

Mathematics

Group Theory

Scientific paper

Let $S$ be a finite semigroup. In this paper we introduce the functions
$\phi_s:S^* \to S^*$, first defined by Rhodes, given by $\phi_s([a_1,a_2
,...,a_n]) = [sa_1,sa_1a_2,..., sa_1a_2 ... a_n]$. We show that if $S$ is a
finite aperiodic semigroup, then the semigroup generated by the functions
$\{\phi_s\}_{s \in S}$ is finite and aperiodic.

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