We give an algebraic proof of the BirmanαBers theoremαan algebraic result whose previous proofs used topology or analysis, and which says that a certain Ε½ . subgroup of finite index in the algebraic mapping class group of an oriented punctured surface is isomorphic to a certain group of automorphism
Subgroups of finite index in certain classes of finitely presented groups
β Scribed by Peter M. Curran
- Publisher
- Elsevier Science
- Year
- 1989
- Tongue
- English
- Weight
- 494 KB
- Volume
- 122
- Category
- Article
- ISSN
- 0021-8693
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π SIMILAR VOLUMES
A sufficient condition is obtained for the residual torsion-free nilpotence of certain finitely presented metabelian groups that arise from a matrix representa-Ε½ . tion developed by Magnus 1939, Ann. of Math. 40, 764α768 for metabelian Ε½ groups. Using this condition and a construction due to Baumsla
We show that if β« is a finitely presented normal subgroup of a product G = G 1 2 of Fuchsian groups which projects nontrivially to each factor, then β« has finite index in G = G . The proof uses the author's previous reduction of the descrip-1 2 tion of normal subdirect products to the abelian case