On finitary properties for fiber products of free semigroups and free monoids (Q2200887)

The authors abstract describes the paper very well: ``We consider necessary and sufficient conditions for finite generation and finite presentability for fiber products of free semigroups and free monoids. We give a necessary and sufficient condition on finite fiber quotients for a fiber product of two free monoids to be finitely generated, and show that all such fiber products are also finitely presented. By way of contrast, we show that fiber products of free semi groups over finite fiber quotients are never finitely generated. We then consider fiber products of free semigroups over infinite semigroups, and show that for such a fiber product to be finitely generated, the quotient must be infinite but finitely generated, idempotent-free, and \(\mathcal{J}\)-trivial. Finally, we construct automata accepting the indecomposable elements of the fiber product of two free monoids/semigroups over free monoid/semigroup fibers, and give a necessary and sufficient condition for such a product to be finitely generated.'' In the introductory section the author makes the connection to preceding related work, mainly about groups, and then gives a detailed overview of the results of the paper. This is helpful since the results and their proofs are technically quite complicated.