Geodesic
Survey of generalized pregroups and a~question of Reinhold Baer
Algebra and discrete mathematics, Tome 13 (2012) no. 2, pp. 220-236.

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There has been recent interest in Stallings' Pregroups. (See [2] and [12].) This paper gives a survey of generalized pregroups. We also answer a question of Reinhold Baer [1] on pregroups and answer a generalization of this question for generalized pregroups.
Keywords: Pregroups, Kushner Axiom K. small cancellation. 
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Anthony M. Gaglione; Seymour Lipschutz; Dennis Spellman. Survey of generalized pregroups and a~question of Reinhold Baer. Algebra and discrete mathematics, Tome 13 (2012) no. 2, pp. 220-236. http://geodesic.mathdoc.fr/item/ADM_2012_13_2_a5/

[1] R. Baer, “Free sums of groups and their generalizations. II; III”, Amer. J. Math., 72 (1950), 625–670 | DOI | MR

[2] Diekert, Duncan, Miasnikov, Geodesic Rewriting Systems and Pregroups, Preprint, 2009

[3] Evans, Trevor, Embeddable and the word problem, Preprint

[4] R. H. Gilman, Generalized small cancellation presentations, preprint, 1998

[5] A. Gaglione, S. Lipschutz, D. Spellman, Note on a Question of Reinhold Baer on Pregroups, II, Preprint, 2011 | Zbl

[6] A. H. M. Hoare, “Pregroups and length functions”, Math. Proc. Camb. Phil. Soc., 104 (1988), 21–30 | DOI | MR | Zbl

[7] A. H. M. Hoare, “On generalizing Stallings' pregroup”, J. of Algebra, 145 (1992), 113–119 | DOI | MR | Zbl

[8] A. H. M. Hoare, On generalizing Stallings' pregroup, II, preprint, 1998 | MR

[9] H. Kushner, On prestars and their universal groups, Ph. D. Thesis, Temple University, 1987

[10] H. Kushne, S. Lipschutz, “A generalization of Stallings' pregroup”, J. of Algebra, 119 (1988), 170–184 | DOI | MR | Zbl

[11] H. Kushne, S. Lipschutz, “On embeddable prees”, J. of Algebra, 160 (1993), 1–15 | DOI | MR | Zbl

[12] Kvaschuk, Miasnikov, Serbin, “Pregroups and the Big Powers Condition”, Algebra and Logic, 48:3 (2009) | DOI | MR | Zbl

[13] S. Lipschutz, “Generalizing the Baer-Stallings pregroup”, Contemporary Math., 169, 1994, 415–430 | DOI | MR | Zbl

[14] S. Lipschutz, W. Shi, “Note on a question of Reinhold Baer on pregroups”, Publ. Inst. Math. (Beograd) (N.S.), 68(82) (2000), 53–58 | MR | Zbl

[15] F. S. Rimlinger, Pregroups and Bass-Serre Theory, Mem. Amer. Math. Soc., no. 361, American Mathematical Society, 1987 | MR | Zbl

[16] J. Stallings, Group Theory and Three-Dimensional Manifolds, Yale Monograph, 4, Yale University Press, 1971 | MR | Zbl