In this article we see that the automorphism group of biholomorphic functions of the upper half plane and the open unit ball in the complex plane is isomorphic to the second projective special linear group over the field of real numbers. [pdf-embedder url="http://gonitsora.mathematics.website/wp-content/uploads/2016/05/automorphisms-upper-half.pdf"] Click here to download. Image Source...

In this article we shall show a peculiar property of $S_5$. We first note that there are several subgroups of $S_n$ isomorphic to $S_{n-1}$. Infact there is one for each $1leq ileq n$ $H_i={sigmain S_n |sigma(i) = i}$ Let $$X={1,2,3,4,5,6}$$. All of the above subgroups have two orbits...