A finite group is called Pn-sequenceable if its nonidentity elements can be listed x1 , x2 , ..., xk so that the product x i x i+i · · · x i+n-1 can be rewritten in at least one nontrivial way for all i. It is shown that Sn , An , Dn are P3-sequenceable, that every finite simple group is P4 -sequenceable, and that every finite group is Ps-sequenceable. It is conjectured that every finite group is P3-sequenceable.
Nielsen, Jeanne, "Rewriteable Sequencings of Groups" (1990). Mathematical Sciences Technical Reports (MSTR). 145.