Abstract: A class of second-type Fuchs group is defined，which is an important generalization of classical modular form. q is acted as a nature number which has no square factor. In the case ofq > 4 ，G(槡q) is defined as the group consisting of matrices in the form of a b槡q 槡( ) c q d ∈SL(2，R) . Then the reduce form of all real positive quadratic form P2 under the action of G(槡q) is discussed. Finally，the relationship between the set of all reduce forms and the fundamental domain under the action of G(槡q) onP2 is given.

Key words: classical group, discrete group, reduce form, fundamental domain

摘要： 定义一类二型Fuchs群，这类Fuchs群是经典模群PSL(2，Z)的重要推广。令q为不含平方因子的自然数， q>4，定义G(槡q)为由形如ab槡q 槡()cqd ∈SL(2，R)的矩阵构成的群。接着，讨论它作用在所有实正定二次型P2 的约化形式。最后，给出所有这些约化形式构成的集合与G(槡q)作用在P2 上的一个基本域的关系。

关键词: 典型群, 离散子群, 约化形式, 基本域