Torsion-free groups and amalgamated products
Authors:
G. Baumslag, A. Karrass and D. Solitar
Journal:
Proc. Amer. Math. Soc. 24 (1970), 688-690
MSC:
Primary 20.52
DOI:
https://doi.org/10.1090/S0002-9939-1970-0260876-9
MathSciNet review:
0260876
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Abstract | References | Similar Articles | Additional Information
Abstract: There exist continuously many finitely generated torsion-free groups which cannot be obtained from the infinite cyclic group by repeatedly forming the free product with an amalgamated subgroup of any two groups already obtained, taking subgroups, and forming ascending unions.
- J. F. Bowers, On composition series of polycyclic groups, J. London Math. Soc. 35 (1960), 433–444. MR 124398, DOI https://doi.org/10.1112/jlms/s1-35.4.433
- P. Hall, Finiteness conditions for soluble groups, Proc. London Math. Soc. (3) 4 (1954), 419–436. MR 72873, DOI https://doi.org/10.1112/plms/s3-4.1.419
- Graham Higman, B. H. Neumann, and Hanna Neumann, Embedding theorems for groups, J. London Math. Soc. 24 (1949), 247–254. MR 32641, DOI https://doi.org/10.1112/jlms/s1-24.4.247
- A. Karrass and D. Solitar, The subgroups of a free product of two groups with an amalgamated subgroup, Trans. Amer. Math. Soc. 150 (1970), 227–255. MR 260879, DOI https://doi.org/10.1090/S0002-9947-1970-0260879-9 A. G. Kuroš, The theory of groups, 2nd ed., GITTL, Moscow, 1953; English transl., Chelsea, New York, 1955. MR 15, 501. MR 17, 124.
- Wilhelm Magnus, Abraham Karrass, and Donald Solitar, Combinatorial group theory: Presentations of groups in terms of generators and relations, Interscience Publishers [John Wiley & Sons, Inc.], New York-London-Sydney, 1966. MR 0207802
- B. H. Neumann, An essay on free products of groups with amalgamations, Philos. Trans. Roy. Soc. London Ser. A 246 (1954), 503–554. MR 62741, DOI https://doi.org/10.1098/rsta.1954.0007
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Additional Information
Keywords:
Torsion-free groups,
amalgamated products,
generalized free products,
presentations,
Reidemeister-Schreier theory,
indecomposable subgroups,
subgroup structure
Article copyright:
© Copyright 1970
American Mathematical Society