MULTIPLICATION TABLES AND WORD-HYPERBOLICITY IN FREE PRODUCTS OF SEMIGROUPS, MONOIDS AND GROUPS

Abstract This article studies the properties of word-hyperbolic semigroups and monoids, that is, those having context-free multiplication tables with respect to a regular combing, as defined by Duncan Gilman [‘Word hyperbolic semigroups’, Math. Proc. Cambridge Philos. Soc. 136 (3) (2004), 513–524]. In particular, preservation word-hyperbolicity under taking free products is considered. Under mild conditions on involved, satisfied, for example, monoids or semigroups, we prove semigroup product two again word-hyperbolic. Analogously, condition uniqueness representation identity element, groups, monoid The methods are language-theoretically general, apply equally well groups $\mathbf {C}$ -multiplication table, where any reversal-closed super- $\operatorname {\mathrm {AFL}}$ . deduce {ET0L}$ indexed has an table.