Forum Math. 12 (2000), 671±712 ( de Gruyter 2000 K. H. Kim, F. W. Roush, and J. B. Wagoner (Communicated by Michael Brin) 1 Introduction We will prove the following theorem stated in [KRW3], thereby completing the third and ®nal step in characterizing inert actions on ®nite sets of periodic points of a primitive subshift of ®nite type XA Y sA constructed from a nonnegative integral matrix A. See [KRW1, KRW2, KRW3] for de®nitions and notation. SGCC Theorem. Assume A is primitive and that h 2 is a positive integer such that for every integer s h there is at least one periodic point of period exactly s. Let be in AutsA jPh . Let g yk GYk for 2 k h, and let osk OSk for 1 k h. Assume that the sign-gyration-compatibility-condition gyk oska2 i 0 ib0 holds for 2 k h. Then there is an element z in InertsA such that GYk z g yk OSk z osk for 2 k h for 1 k h While the method of proof is somewhat similar to the one used in proving the GY Theorem and OS Theorem of [KRW3], a new technique called the Enlargement Method
Forum Mathematicum – de Gruyter
Published: Sep 6, 2000
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