The Product Replacement Graph on Generating Triples of Permutations
نویسندگان
چکیده
We prove that the product replacement graph on generating 3-tuples of An is connected for n ≤ 11. We employ an efficient heuristic based on [P1] which works significantly faster than brute force. The heuristic works for any group. Our tests were confined to An due to the interest in Wiegold’s Conjecture, usually stated in terms of T -systems (see [P2]). Our results confirm Wiegold’s Conjecture in some special cases and are related to the recent conjecture of Diaconis and Graham [DG]. The work was motivated by the study of the product replacement algorithm (see [CLMNO,P2]).
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