Embeddings into simple free products

Author:
David Meier

Journal:
Proc. Amer. Math. Soc. **93** (1985), 387-392

MSC:
Primary 20E06; Secondary 20E32, 20F10

DOI:
https://doi.org/10.1090/S0002-9939-1985-0773986-5

MathSciNet review:
773986

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Abstract | References | Similar Articles | Additional Information

Abstract: We prove that a countable group can be embedded into a two-generator simple group which is an amalgamated free product of groups and , where and are free groups on two generators. is also the product of two commuting free subgroups. If has solvable word problem, then we can construct a recursive presentation for .

**[1]**R. Camm,*Simple free products*, J. London Math. Soc.**28**(1953), 66-76. MR**0052420 (14:616f)****[2]**W. W. Boone and G. Higman,*An algebraic characterization of the solvability of the word problem*, J. Austral. Math. Soc.**18**(1974), 41-53. MR**0357625 (50:10093)****[3]**A. P. Goryushkin,*Imbedding of countable groups in two-generator groups*, Mat. Zametki**16**(1974), 231-235. MR**0382456 (52:3339)****[4]**R. C. Lyndon and P. E. Schupp,*Combinatorial group theory*, Springer-Verlag, Heidelberg, 1977. MR**0577064 (58:28182)****[5]**W. Magnus, A. Karrass and D. Solitar,*Combinatorial group theory*, Wiley, New York, 1966.**[6]**D. Meier,*A note on simple free products*, Houston J. Math.**9**(1983), 501-504. MR**732241 (86b:20030)****[7]**P. E. Schupp,*Embeddings into simple groups*, J. London Math. Soc.**13**(1976), 90-94. MR**0401932 (53:5758)****[8]**R. J. Thompson,*Embeddings into finitely generated simple groups which preserve the word problem*, Word Problems. II, North-Holland, Amsterdam, 1980, pp. 401-441. MR**579955 (81k:20050)**

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DOI:
https://doi.org/10.1090/S0002-9939-1985-0773986-5

Article copyright:
© Copyright 1985
American Mathematical Society