✦ LIBER ✦
A Family of Markov Shifts (Almost) Classified by Periodic Points
✍ Scribed by Thomas Ward
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 262 KB
- Volume
- 71
- Category
- Article
- ISSN
- 0022-314X
No coin nor oath required. For personal study only.
✦ Synopsis
Let G be a finite group, and let
Using recent work by Crandall, Dilcher and Pomerance on the Fermat quotient, we show the following: if G is abelian, and the order of G is not divisible by 1024, nor by the square of any Wieferich prime larger than 4_10 12 , and H is any abelian group for which 7 G has the same periodic point data as 7 H , then G is isomorphic to H. This result may be viewed as an example of the ``rigidity'' properties of higherdimensional Markov shifts with zero entropy.