The algorithmic theory of finitely generated metabelian groups

Abstract

Algorithms are constructed which, when an explicit presentation of a finitely generated metabelian group G in the variety X 2 is given, produce finitary presentations for the derived subgroup G' , the centre Z(G), the Fitting subgroup Fit(G) , and the Frattini subgroup (0(G) . Additional algorithms of independent interest are developed for commutative algebra which construct the associated set of primes Ass(M) of a finitely generated module M over a finitely generated commutative ring R, and the intersection (PR(M) of the maximal submodules of M.