Groups, ends and trees: exercises I Michele Triestino 2015-07-21 Exercise 1. Show that SL(n, Z) is generated by the transvections: these are the matrices with 1's on the diagonal and one other entry equal to 1 and all the others 0. ... Show that the fundamental group of a bouquet of n circles is the free group over an alphabet S of size n: #S = n. More generally, what is the fundamental group of a finite graph? ... Prove that the quotient of a finitely generated group is finitely generated. ...