Two-Element Generation of Orthogonal Groups over Finite Fields
✍ Scribed by H. Ishibashi; A.G. Earnest
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 294 KB
- Volume
- 165
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
✦ Synopsis
Minimal sets of generators of the orthogonal groups on nonsingular quadratic spaces over a finite field are studied. All such orthogonal groups are shown to be generated by two elements, with the possible exception of two low-dimensional cases. 1994 Academic Press, Inc.
📜 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.
Given a global field F and a prime number p we characterize the finitely generated pro-p closed subgroups of the absolute Galois group of F.
Let A be a finite abelian group such that there is an elliptic curve defined over a finite field F q with E(F q )$A. We will determine the possible group structures E(F q k) as E varies over all elliptic curves defined over F q with E(F q )$A.
In this paper we study the characteristic polynomials and the rational point group structure of supersingular varieties of dimension two over finite fields. Meanwhile, we also list all L-functions of supersingular curves of genus two over ކ 2 and determine the group structure of their divisor clas