Equivalence classes of matrices over a finite field
Let Fq=GF(q) denote the finite field of order q and F(m,q) the ring of m×m matrices over Fq. Let Ω be a group of permutations of Fq. If A,BϵF(m,q) then A is equivalent to B relative to Ω if there exists ϕϵΩ such that ϕ(A)=B where ϕ(A) is computed by substitution. Formulas are given for the number of...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
1979-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171279000387 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832555959469211648 |
|---|---|
| author | Gary L. Mullen |
| author_facet | Gary L. Mullen |
| author_sort | Gary L. Mullen |
| collection | DOAJ |
| description | Let Fq=GF(q) denote the finite field of order q and F(m,q) the ring of m×m matrices over Fq. Let Ω be a group of permutations of Fq. If A,BϵF(m,q) then A is equivalent to B relative to Ω if there exists ϕϵΩ such that ϕ(A)=B where ϕ(A) is computed by substitution. Formulas are given for the number of equivalence classes of a given order and for the total number of classes induced by a cyclic group of permutations. |
| format | Article |
| id | doaj-art-d499ffbad90c48408358a4796405dad7 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1979-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-d499ffbad90c48408358a4796405dad72025-02-03T05:46:53ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251979-01-012348749110.1155/S0161171279000387Equivalence classes of matrices over a finite fieldGary L. Mullen0Department of Mathematics, The Pennsylvania State University, Sharon 16146, Pennsylvania, USALet Fq=GF(q) denote the finite field of order q and F(m,q) the ring of m×m matrices over Fq. Let Ω be a group of permutations of Fq. If A,BϵF(m,q) then A is equivalent to B relative to Ω if there exists ϕϵΩ such that ϕ(A)=B where ϕ(A) is computed by substitution. Formulas are given for the number of equivalence classes of a given order and for the total number of classes induced by a cyclic group of permutations.http://dx.doi.org/10.1155/S0161171279000387equivalencepermutationautomorphismfinite field. |
| spellingShingle | Gary L. Mullen Equivalence classes of matrices over a finite field International Journal of Mathematics and Mathematical Sciences equivalence permutation automorphism finite field. |
| title | Equivalence classes of matrices over a finite field |
| title_full | Equivalence classes of matrices over a finite field |
| title_fullStr | Equivalence classes of matrices over a finite field |
| title_full_unstemmed | Equivalence classes of matrices over a finite field |
| title_short | Equivalence classes of matrices over a finite field |
| title_sort | equivalence classes of matrices over a finite field |
| topic | equivalence permutation automorphism finite field. |
| url | http://dx.doi.org/10.1155/S0161171279000387 |
| work_keys_str_mv | AT garylmullen equivalenceclassesofmatricesoverafinitefield |