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## Inert actions on periodic points

### K. H. Kim, F. W. Roush and J. B. Wagoner

**Abstract.**
The action of inert automorphisms on finite sets of periodic points
of mixing subshifts of finite type is
characterized in terms of the sign-gyration-compatibility condition.
The main technique used is variable length
coding combined with a ``nonnegative algebraic K-theory" formulation
of state splitting and merging. One
application gives a counterexample to the Finite Order Generation
Conjecture by producing examples of infinite
order inert automorphisms of mixing subshifts of finite type which
are not products of finite order
automorphisms.

*Copyright 1997 American Mathematical Society*

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#### Article Info

- ERA Amer. Math. Soc.
**03** (1997), pp. 55-62
- Publisher Identifier: S 1079-6762(97)00024-3
- 1991
*Mathematics Subject Classification*. Primary 54H20, 57S99, 20F99
- Received by the editors October 25, 1996
- Posted on July 30, 1997
- Communicated by Douglas Lind
- Comments (When Available)

**K. H. Kim**

Department of Mathematics, Alabama State University, Montgomery,
Alabama 36101

*E-mail address:* `kkim@asu.alasu.edu`

**F. W. Roush**

Department of Mathematics, Alabama State University, Montgomery,
Alabama 36101

*E-mail address:* `kkim@asu.alasu.edu`

**J. B. Wagoner**

Department of Mathematics, UCB, Berkeley, California 94720

*E-mail address:* `wagoner@math.berkeley.edu`

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