线性齐次型上的周期作用

Periodic Acts on a Linear Homogeneous Pattern

对于一个给定的整系数线性齐次型,考虑整数环上一般线性群中一个线性变换对该线性齐次型的系数的作用。特别地,由定义在数字半群上的线性齐次型的角度出发给出了一个充分条件,如果一般线性群中一个有限周期线性变换满足该条件则存在一个与之共轭线性变换,使得该共轭线性变换生成的循环群作用于一个容许型后所得一族型都是容许型。此外,还给出了一般线性群中一个线性变换相对某个型是有限周期作用的充要条件。

For a linear homogeneous pattern, linear transformations in the general group over integers act on its coefficients are considered.From the view of patterns on numerical semigroups, a sufficient condition is given： under the condition, an ele-ment of finite period in the general group has a conjugation , such that the resulted patterns remain admissible by the conjugation generated cyclic subgroup acting on an admissible pattern .Moreover, an equivalent condition for an element in the general group that is finitely periodic relative to a pattern is obtained .