Geodesic
Embedding Theorems for Countable Groups
Canadian journal of mathematics, Tome 22 (1970) no. 4, pp. 827-835

Voir la notice de l'article provenant de la source Cambridge University Press

A group P is said to be a CEF-group if, for every countable group G, there is a factor group of P which contains a subgroup isomorphic to G. It was shown by Higman, Neumann, and Neumann [5] that the free group of rank two is a CEF-group. More recently, Levin [6] proved that if P is the free product of two cyclic groups, not both of order two, then P is a CEF-group. Later, Hall [3] gave an alternative proof of Levin's result.In this paper we give a new proof of Levin's result (Theorem 2). The proof given yields information about the factor group H of P in which a given countable group G is embedded; for example, if G is given by a recursive presentation (this concept is denned in [4]), then a recursive presentation is obtained for H, and certain decision problems (in particular, the word problem) are solvable for the recursive presentation obtained for H if and only if they are solvable for the given recursive presentation of G. 
McCool, James. Embedding Theorems for Countable Groups. Canadian journal of mathematics, Tome 22 (1970) no. 4, pp. 827-835. doi: 10.4153/CJM-1970-093-9
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[1] 1. Britton, J. L., Solution of the word problem for certain types of groups. I, Proc. Glasgow Math. Assoc. 8 (1956), 45–54. Google Scholar

[2] 2. Britton, J. L., Solution of the word problem for certain types of groups. II, Proc. Glasgow Math. Assoc. 3 (1956), 68–90. Google Scholar

[3] 3. Hall, P., Embedding theorems for countable groups, p. 3 in Some problems and results in the theory of groups. II (Notes of a mini-conference held in Oxford, August 12th and 13th, 1966), Oxford, December, 1966. Google Scholar

[4] 4. Higman, G., Subgroups of finitely presented groups, Proc. Roy. Soc. Ser. A 262 (1961), 455–475. Google Scholar

[5] 5. Higman, G., Neumann, B. H., and Hanna, Neumann, Embedding theorems for groups, J. London Math. Soc. 24 (1949), 247–254. Google Scholar

[6] 6. Levin, F., Factor groups of the modular group, J. London Math. Soc. 43 (1968), 195–203. Google Scholar

[7] 7. McCool, J., Elements of finite order in free product sixth-groups, Glasgow Math. J. 9 (1968), 128–145. Google Scholar

[8] 8. McCool, J., The order problem and the power problem in free product sixth-groups, Glasgow Math. J. 10 (1969), 1–9. Google Scholar

[9] 9. Miller, C. F., III and Schupp, P. E., Embeddings into Hopfian groups, Notices Amer. Math. Soc. 16 (1969), 654. Google Scholar

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