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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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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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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 344 (1994), 629-648
  • MSC: Primary 20F10; Secondary 13L05
  • DOI: https://doi.org/10.1090/S0002-9947-1994-1202419-X
  • MathSciNet review: 1202419