Let An（R） be the set of symmetric matrices over Z/p^kZ with order n, where n 〉 2, p is a prime, p 〉 2 and p≡1（mod4）, k 〉 1. By determining the normal form of n by n symmetric matrices over Z/p^kZ, we compute t...Let An（R） be the set of symmetric matrices over Z/p^kZ with order n, where n 〉 2, p is a prime, p 〉 2 and p≡1（mod4）, k 〉 1. By determining the normal form of n by n symmetric matrices over Z/p^kZ, we compute the number of the orbits of An（R） and then compute the order of the orthogonal group determined by the special symmetric matrix. Finally we get the number of the symmetric matrices which are in the same orbit with the special symmetric matrix.展开更多
基金the Key Project of Chinese Ministry of Education (03060)
文摘Let An（R） be the set of symmetric matrices over Z/p^kZ with order n, where n 〉 2, p is a prime, p 〉 2 and p≡1（mod4）, k 〉 1. By determining the normal form of n by n symmetric matrices over Z/p^kZ, we compute the number of the orbits of An（R） and then compute the order of the orthogonal group determined by the special symmetric matrix. Finally we get the number of the symmetric matrices which are in the same orbit with the special symmetric matrix.
