A note of equivalence classes of matrices over a finite field

J. V. Brawley and Gary L. Mullen

International Journal of Mathematics and Mathematical Sciences, 1981, vol. 4, 1-9

Abstract:

Let F q m × m denote the algebra of m × m matrices over the finite field F q of q elements, and let Ω denote a group of permutations of F q . It is well known that each ϕ ϵ Ω can be represented uniquely by a polynomial ϕ ( x ) ϵ F q [ x ] of degree less than q ; thus, the group Ω naturally determines a relation ∼ on F q m × m as follows: if A , B ϵ F q m × m then A ∼ B if ϕ ( A ) = B for some ϕ ϵ Ω . Here ϕ ( A ) is to be interpreted as substitution into the unique polynomial of degree < q which represents ϕ .

In an earlier paper by the second author [1], it is assumed that the relation ∼ is an equivalence relation and, based on this assumption, various properties of the relation are derived. However, if m ≥ 2 , the relation ∼ is not an equivalence relation on F q m × m . It is the purpose of this paper to point out the above erroneous assumption, and to discuss two ways in which hypotheses of the earlier paper can be modified so that the results derived there are valid.

Date: 1981
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/4/913968.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/4/913968.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:913968

DOI: 10.1155/S0161171281000161

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().