Author | Neumann, Hanna. author |
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Title | Varieties of Groups [electronic resource] / by Hanna Neumann |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1967 |
Connect to | http://dx.doi.org/10.1007/978-3-642-88599-0 |
Descript | XII, 194 p. online resource |
1. The Basic Facts -- 1. Preliminaries -- 2. Words, Laws, Verbal Subgroups -- 3. Relatively Free Groups -- 4. Varieties -- 5. Varieties as Closed Classes of Groups -- 6. The n-Generator Groups and the n-Variable Laws of a Variety -- 7. Discrimination and Residual Properties -- 8. Verbal Products -- 2. Product Varieties -- 1. The Algebra of Varieties -- 2. Wreath Products and Discrimination -- 3. The Uniqueness of Factorization -- 4. Some Classes of Indecomposable Varieties -- 5. Product Varieties Generated by a Finitely Generated Group -- 6. Residual Properties of the Free Groups of Product Varieties -- 3. Nilpotent Varieties -- 1. Summary of Properties of Nilpotent Groups -- 2. Residual Properties -- 3. A Lemma on Words with an Application to Free Products -- 4. The Laws of a Nilpotent Variety and Related Topics -- 5. Generating Groups of Finite Rank -- 6. The Variety of All Metabelian Nilpotent Groups of Class c -- 4. Miscellaneous Properties of Relatively Free Groups -- 1. Remarks on Automorphisms and the Hopf Property -- 2. Free Subgroups of Free Groups -- 3. Theorems Like Auslander and Lyndonโs: the Schreier Property -- 4. The Splitting Property; Direct Decomposability -- 5. The Laws of Finite Groups -- 1. Critical Groups and Cross Varieties -- 2. The Theorem of Oates and Powell -- 3. Critical Groups and Subvarieties -- 4. Critical p-Groups and Locally Finite Varieties; a Summary of Developments -- References -- Author Index