The algorithmic theory of finitely generated metabelian groups

Baumslag, Gilbert; Cannonito, Frank B.; Robinson, Derek J. S.

doi:10.1090/S0002-9947-1994-1202419-X

The algorithmic theory of finitely generated metabelian groups
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by Gilbert Baumslag, Frank B. Cannonito and Derek J. S. Robinson PDF

Trans. Amer. Math. Soc. 344 (1994), 629-648 Request permission

Abstract:

Algorithms are constructed which, when an explicit presentation of a finitely generated metabelian group G in the variety ${\mathcal {A}^2}$ is given, produce finitary presentations for the derived subgroup $G\prime$, the centre $Z(G)$, the Fitting subgroup $\operatorname {Fit}(G)$, and the Frattini subgroup $\varphi (G)$. Additional algorithms of independent interest are developed for commutative algebra which construct the associated set of primes $\operatorname {Ass}(M)$ of a finitely generated module M over a finitely generated commutative ring R, and the intersection ${\varphi _R}(M)$ of the maximal submodules of M.

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