Permutation matrices and matrix equivalence over a finite field

[摘要] LetF=GF(q)denote the finite field of orderqandFm×nthe ring ofm×nmatrices overF. Let?nbe the set of all permutation matrices of ordernoverFso that?nis ismorphic toSn. IfΩis a subgroup of?nandA,BϵFm×nthenAis equivalent toBrelative toΩif there existsPϵ?nsuch thatAP=B. In sections 3 and 4, ifΩ=?nformulas are given for the number of equivalence classes of a given order and for the total number of classes. In sections 5 and 6 we study two generalizations of the above definition.

[学科分类] 数学（综合）