Mobius Transformations

In mathematics, the modular group is the projective special linear group PSL ⁡ ( 2 , Z ) {-displaystyle -operatorname {PSL} (2,-mathbb {Z} )} {-displaystyle ... Definition · Number-theoretic properties · Group-theoretic properties

This article is about a particular group, i.e., a group unique upto isomorphism. View specific information (such as linear representation ... 1Definition · 1.1Definition by presentation · 2Arithmetic functions · 3Group properties

We will give two proofs that G = SL2(Z), one algebraic and the other geometric. For the algebraic proof, we start by writing down the effect of S and Tn on a ...

Definition (Group Action). A group action of G on a set S is a map G × S -→ S which satisfies the following axioms: a. For any s ∈ S, ...

Here is how I tackled this when I was given it as a homework problem: We prove that. |SL2(Z/peZ)|=p3e(1−1p2). by induction.

I am trying to prove that the the natural map from the special linear group SL2(Z) to the special linear group SL2(Z/nZ) is surjective. Clearly, ...

The group SL(2,Z) is the group of two-by-two matrices with integer entries and determinant one. This is a very simple definition. Yet its ...

We now prove statement (a). Consider the set Λτ = Zτ + Z ⊂ C, which is a discrete subset of C. We can therefore choose λ = c0τ +d0 with c0,d0 ∈ Z not both ...

The modular group is the subgroup SL(2, Z) of the matrix group SL(2, R) consisting of matrices with integer entries and determinant 1. There is an important ...

SL2(ℝ) 編輯 ... 它是一個三維李群，在幾何、拓撲、表示論及物理中有重要應用． 與 SL₂(ℝ) 密切相關的是射影線性群 PSL₂(ℝ)。這是將 SL₂(ℝ) 中每個元素與它的負元素等同得到的 ...