Structure of Some Pregroups and Length Functions
Journal of Advances in Mathematics and Computer Science · pp. 1–12 · Published 1 Aug 2017
10.9734/JAMCS/2017/34918Abstract
The concept of Pregroups was introduced by Stallings in 1971. Subsequently the concept of Pregroups was developed by many other researchers. Stallings originally defined a set with a binary operation satisfying five axioms, namely, P1, P2, P3, P4, and P5. It has been proved later that P3 is a consequence of the other axioms. Stallings has also linked this construction of a Pregroup to Free Product of Groups. This construction is developed to include a new axiom called P6, which enabled to define a length function on the universal group of Pregroups. Applications of Pregroups with length functions led to direct proof of many other problems in combinatorial group theory.
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