Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8897595 | Journal of Pure and Applied Algebra | 2018 | 8 Pages |
Abstract
Let Fq be the finite field with q elements, p=char(Fq). The group GL2(Fq) acts naturally in the set of irreducible polynomials over Fq of degree at least 2. In this paper we are interested in the characterization and number of the irreducible polynomials that are fixed by the elements of a subgroup H of GL2(Fq). We make a complete characterization of the fixed polynomials in the case when H has only elements of the form (1b01), corresponding to translations xâ¦x+b and, as a consequence, the case when H is a p-subgroup of GL2(Fq). This paper also contains alternative solutions for the cases when H is generated by an element of the form (a001), obtained by Garefalakis (2010) and H=PGL2(Fq), obtained by Stichtenoth and Topuzoglu (2011).
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Lucas Reis,