Geodesic
Note on Generalizing Pregroups
Publications de l'Institut Mathématique, _N_S_45 (1989) no. 59, p. 77

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Let $P$ be a pree which satisfies the first four axioms of Stallings' pregroup. Then the following three axioms are equivalent: \item{[K]} If $ab, bc$ and $cd$ are defined, and $(ab)(cd)$ is defined, then $(ab)c$ or $(bc)d$ is defined. \item{[L]} Suppose $V=[x, y]$ is reduced and suppose $y=ab=cd$ where $xa$ and $xc$ are defined. Then $a^{-1}c$ is defined. \item{[M]} Suppose $W=[x, y, z]$ is reduced. Then $W$ is not reducible to a word of length one.
Classification : 20E06 
@article{PIM_1989_N_S_45_59_a10,
     author = {Seymour Lipschutz},
     title = {Note on {Generalizing} {Pregroups}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {77 },
     publisher = {mathdoc},
     volume = {_N_S_45},
     number = {59},
     year = {1989},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1989_N_S_45_59_a10/}
}
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Seymour Lipschutz. Note on Generalizing Pregroups. Publications de l'Institut Mathématique, _N_S_45 (1989) no. 59, p. 77 . http://geodesic.mathdoc.fr/item/PIM_1989_N_S_45_59_a10/