INTRANSITIVE ACTION OF THE GROUP PSL ( 2 , Z ) ON A SUBSET Q ∗ ( √ k 2 m ) OF Q ( √ m )
نویسنده
چکیده
It is well-known that PSL(2, Z) is the group generated by the linear-fractional transformations x : z → − z and y : z → z−1 z , which satisfy the relations x = y = 1. We denote this modular group by G = 〈x, y : x = y = 1〉. Let n = km, where m is a square-free positive integer and k is any non zero integer. Then Q∗( √ n) = { √ n c : a, c and b = a −n c are integers and (a, b, c) = 1} is a G-subset of the real quadratic field Q( √ m) for all k [8]. 32 M. Aslam Malik, S.M. Husnine & Abdul Majeed In this paper we show that for each non-square positive integer n > 2, the action of the group G on Q∗( √ n) is intransitive.
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