Nilpotent Quotients of Associative [Formula: see text]-Algebras and Augmentation Quotients of Baumslag-Solitar Groups

We describe the functionality of the package zalgs for the computer algebra system GAP. The package contains an implementation of the nilpotent quotient algorithm for finitely presented associative [Formula: see text]-algebras described in [3]. As an application of this algorithm we calculate augmentation quotients, i.e. successive quotients of powers of the augmentation ideal I(G) of the integral group ring [Formula: see text], where G is a finitely presented group. We apply these methods to obtain conjectures for augmentation quotients of the Baumslag-Solitar groups BS(m, n) with [Formula: see text] equal to 0, 1 or a prime p.