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A Note on the Classical Dickson Invariants.
- Source :
-
Algebra Colloquium . Sep2010, Vol. 17 Issue 3, p415-424. 10p. - Publication Year :
- 2010
-
Abstract
- Let 픽q be the finite field with q elements, where q is a power of some prime p. In the classical paper [2], Dickson defined the polynomial $[e_1,e_2,\dots,e_n]:=\det (x_j^{q^{e_i}})_{n\times n} \in {\Bbb F}_q[x_1,x_2,\dots,x_n]$, where e1,..., en are non-negative integers. He observed that any [e1,..., en] is divisible by [0,1,...,n-1], and the quotient is GLn(픽q)-invariant. He then went on to show that one can pick n of these invariants to generate the entire invariant subring of GLn(픽q). In this paper, we answer the following two natural questions: How to express any given [e1,..., en]/[0,1,...,n-1] in terms of the fundamental generators? In general, when does [e1,..., en] divide [f1,..., fn]? The answers are Theorems 1.2 and 1.3, respectively. [ABSTRACT FROM AUTHOR]
- Subjects :
- *FINITE groups
*POLYNOMIALS
*GROUP theory
*ALGEBRA
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 10053867
- Volume :
- 17
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Algebra Colloquium
- Publication Type :
- Academic Journal
- Accession number :
- 51993885
- Full Text :
- https://doi.org/10.1142/S1005386710000398