Titlebook: Lectures on Finitely Generated Solvable Groups; Katalin A. Bencsath,Marianna C. Bonanome,Marcos Zy Book 2013 Katalin A. Bencsath, Marianna

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,The Bieri–Strebel Theorems,ented groups with an infinite cyclic quotient: such a group is either an ascending .-extension or else contains a free group of rank 2. An immediate consequence of the second theorem is that a solvable finitely presented group is either finite or else is virtually an ascending .-extension of a finitely generated solvable group.

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Tools: Presentations and Their Calculus,We introduce group presentations, present Von Dyck’s lemma and Tietze’s theorem on their transformations. We bring in an important result by B.H. Neumann about finitely presentable groups.

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An Embedding Theorem for Finitely Generated Metabelian Groups,The theorem we present, due to G. Baumslag, is a milestone in the study of metabelian group theory and is a refinement of a 1961 result by Higman. It states that any finitely generated metabelian group can be embedded in a finitely presented metabelian group.