Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Embeddings into simple free products

Author: David Meier
Journal: Proc. Amer. Math. Soc. 93 (1985), 387-392
MSC: Primary 20E06; Secondary 20E32, 20F10
MathSciNet review: 773986
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We prove that a countable group $ G$ can be embedded into a two-generator simple group $ S$ which is an amalgamated free product of groups $ G * {F_1}$ and $ F$, where $ F$ and $ {F_1}$ are free groups on two generators. $ S$ is also the product of two commuting free subgroups. If $ G$ has solvable word problem, then we can construct a recursive presentation for $ S$.

References [Enhancements On Off] (What's this?)

  • [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)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 20E06, 20E32, 20F10

Retrieve articles in all journals with MSC: 20E06, 20E32, 20F10

Additional Information

Article copyright: © Copyright 1985 American Mathematical Society

American Mathematical Society