二面体群D_n与Z_n上的一类全向置换

The Dihedral Group D_n and a kind of Omni_Direction Permutations on Z_n

本文证明了当n为奇整数时,二面体群Dn的每个反射(即保持某个顶点不变的翻转)Si产生一个modn的全向置换,并且这样的全向置换必然是线性函数。

This paper proves that when n is odd, any reflection of the dihedral group Dn generates an omnidirection permutation of Zn,and proves that these omnidirection permutations are also linear functions on Zn.