Free Group Rings.

Intro -- Table of Contents -- Preface -- Chapter I: Magnus Embeddings and Free Differential Calculus -- 1. Some faithful 2 X 2 matrix representations -- 2. Free differential calculus -- 3. The fundamental theorem of free group rings -- 4. The Poincaré-Birkhoff-Witt Theorem -- Chapter II: Applications of Magnus Embedding -- 1. Some properties of F/R' -- 2. Some algorithmic problems in F/R' -- 3. Faithfulness of relation modules -- 4. Residual nilpotence of F/R' -- Chapter III: Fox Subgroups of Free Groups -- 1. A faithful matrix representation of F/F(n,R) -- 2. Identification of F(2,R) -- 3. Identification of F(n,R) (F/R finite) -- 4. A filtration of the lower central series of F -- 5. A solution of the Fox problem -- 6. Structure of Fox modules -- 7. The centre of F/F(n,R), n ≥ 2 -- Chapter IV: Dimension Subgroups -- 1. Sjogren's theorem -- 2. A counter-example due to rips -- 3. Some preliminary results on dimension subgroups -- 4. Dimension subgroups of metabelian groups -- 5. Structure of the fourth dimension subgroup -- 6. Dimension subgroups of metabelian p-groups -- Chapter V: Generalized Magnus Ernbeddings -- 1. A faithful matrix representation of ~F/~~ (1. A faithful matrix representation of ~F/nx (x ≤ s -- 2. A faithful matrix representation of zF/x1 ... xn -- 3. Residual nilpotence of F/F n {1+x 1 ···xn) -- 4. Identification of F n (1+x1 ···xn) for small n -- 5. Some applications of the generalized embeddings -- 6. The problem section -- Bibliography.

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