Polynomial maps over finite fields and residual finiteness of mapping tori of group endomorphisms
β Scribed by Alexander Borisov; Mark Sapir
- Publisher
- Springer-Verlag
- Year
- 2004
- Tongue
- English
- Weight
- 294 KB
- Volume
- 160
- Category
- Article
- ISSN
- 0020-9910
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Let F be a finite field. We apply a result of Thierry Berger (1996, Designs Codes Cryptography, 7, 215-221) to determine the structure of all groups of permutations on F generated by the permutations induced by the linear polynomials and any power map which induces a permutation on F.
Let k=GF(q) be the finite field of order q. Let f 1 (x), f 2 (x) # k[x] be monic relatively prime polynomials satisfying n=deg f 1 >deg f 2 0 and f 1 (x)Γf 2 (x){ g 1 (x p )Γg 2 (x p ) for any g 1 (x), g 2 (x) # k[x]. Write Q(x)= f 1 (x)+tf 2 (x) and let K be the splitting field of Q(x) over k(t). L