THE ALGORITHMIC THEORY OF FINITELY GENERATED METABELIAN-GROUPS

Algorithms are constructed which, when an explicit presentation of a f initely generated metabelian group G in the variety A2 is given, produ ce finitary presentations for the derived subgroup G', the centre Z(G) , the Fitting subgroup Fit(G), and the Frattini subgroup phi(G). Addit ional algorithms of independent interest are developed for commutative algebra which construct the associated set of primes Ass(M) of a fini tely generated module M over a finitely generated commutative ring R, and the intersection phi(R)(M) of the maximal submodules of M.