Author | Baumslag, Gilbert. author |
---|---|
Title | Topics in Combinatorial Group Theory [electronic resource] / by Gilbert Baumslag |
Imprint | Basel : Birkhรคuser Basel : Imprint: Birkhรคuser, 1993 |
Connect to | http://dx.doi.org/10.1007/978-3-0348-8587-4 |
Descript | VIII, 170 p. online resource |
I History -- 1. Introduction -- 2. The beginnings -- 3. Finitely presented groups -- 4. More history -- 5. Higmanโs marvellous theorem -- 6. Varieties of groups -- 7. Small Cancellation Theory -- II The Weak Burnside Problem -- 1. Introduction -- 2. The Grigorchuk-Gupta-Sidki groups -- 3. An application to associative algebras -- III Free groups, the calculus of presentations and the method of Reidemeister and Schreier -- 1. Frobeniusโ representation -- 2. Semidirect products -- 3. Subgroups of free groups are free -- 4. The calculus of presentations -- 5. The calculus of presentations (continued) -- 6. The Reidemeister-Schreier method -- 7. Generalized free products -- IV Recursively presented groups, word problems and some applications of the Reidemeister-Schreier method -- 1. Recursively presented groups -- 2. Some word problems -- 3. Groups with free subgroups -- V Affine algebraic sets and the representative theory of finitely generated groups -- 1. Background -- 2. Some basic algebraic geometry -- 3. More basic algebraic geometry -- 4. Useful notions from topology -- 5. Morphisms -- 6. Dimension -- 7. Representations of the free group of rank two in SL(2,C) -- 8. Affine algebraic sets of characters -- VI Generalized free products and HNN extensions -- 1. Applications -- 2. Back to basics -- 3. More applicatone -- 4. Some word, conjugacy and isomorphism problems -- VII Groups acting on trees -- 1. Basic definitions -- 2. Covering space theory -- 3. Graphs of groups -- 4. Trees -- 5. The fundamental group of a graph of groups -- 6. The fundamental group of a graph of groups (continued) -- 7. Group actions and graphs of groups -- 8. Universal covers -- 9. The proof of Theorem 2 -- 10. Some consequences of Theorem 2 and 3 -- 11. The tree of SL2