Residual properties of free groups and probabilistic methods
نویسندگان
چکیده
Let w be a non-trivial word in two variables. We prove that the probability that two randomly chosen elements x, y of a nonabelian finite simple group S satisfy w(x, y) = 1 tends to 0 as |S| → ∞. As a consequence, we obtain a new short proof of a well-known conjecture of Magnus concerning free groups, as well as some applications to profinite groups. Research partially supported by NSERC grant A7171 for J.D., the Hungarian Academy of Sciences grant AKP 96/2-675 for L.P., NSF grants CCR-9503430, CCR-9731799 for Á. S. and a grant from the Israel Science Foundation for A. S. 1991 Mathematics Subject Classification: 20D06, 20E05, 20E26, 20P05.
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تاریخ انتشار 2005