I was making a diagram of different types of groups; finite /infinite, cyclic / non-cyclic, finitely generated / inifinitely generated, but realized that I didn't have any examples og infinite groups, that are both finitely generated and non -abelian. Does anyone have any examples? :)
I was thinking about creating an example based on matrices and matrix multiplication, but I didn't get very far. I know that since I am looking for a finitely generated group, It must be countable.