EMIS ELibM Electronic Journals PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)
Vol. 45(59), pp. 77--80 (1989)

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NOTE ON GENERALIZING PREGROUPS

Seymour Lipschutz

Department of Mathematics, Temple University, Philadelphia, PA 19122, USA

Abstract: 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 (MSC2000): 20E06

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Electronic fulltext finalized on: 2 Nov 2001. This page was last modified: 16 Nov 2001.

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