A normal-form theorem for monoids and groups with the single relation xy ↔ yx
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چکیده
The word problem for confluent Thue systems is linear-time and for almost confluent systems it is PSPACE-complete. Here we consider a single length-preserving rule, of the form xy ↔ yx, whose word problem could turn out to be tractable. A search for normal forms leads to the conjecture that if xy ↔ xy then m = p and n = q. We prove a stronger version of this: in a group G with the single relator xyxy, where x and y are positive words, if xy = 1 in G then m = n = 0.
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تاریخ انتشار 2007