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A new look at finitely generated metabelian groups. (English) Zbl 1283.20032
Fine, Benjamin (ed.) et al., Computational and combinatorial group theory and cryptography. AMS special sessions: Computational algebra, groups, and applications, University of Nevada, Las Vegas, NV, USA, April 30–May 1, 2011. Mathematical aspects of cryptography and cyber security, Cornell University, Ithaca, NY, USA, September 10–11, 2011. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-7563-6/pbk; 978-0-8218-9404-0/ebook). Contemporary Mathematics 582, 21-37 (2012).
Summary: A group is metabelian if its commutator subgroup is Abelian. For finitely generated metabelian groups, classical commutative algebra, algebraic geometry and geometric group theory, especially the latter two subjects, can be brought to bear on their study. The object of this paper is to describe some of the new ideas and open problems that arise.
For the entire collection see [Zbl 1253.20001].

20F16 Solvable groups, supersolvable groups
20F05 Generators, relations, and presentations of groups
20F10 Word problems, other decision problems, connections with logic and automata (group-theoretic aspects)
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