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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



The algorithmic theory of finitely generated metabelian groups

Authors: Gilbert Baumslag, Frank B. Cannonito and Derek J. S. Robinson
Journal: Trans. Amer. Math. Soc. 344 (1994), 629-648
MSC: Primary 20F10; Secondary 13L05
MathSciNet review: 1202419
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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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Article copyright: © Copyright 1994 American Mathematical Society