Definable sets of generators in maximal cofinitary groups

A group G⩽Sym(N) is cofinitary if g has finitely many fixed points for every g∈G except the identity element. In this paper, we discuss the definability of maximal cofinitary groups and some related structures. More precisely, we show the following two results:(1)Assuming V=L, there is a set of permutations on N which generates a maximal cofinitary group.(2)Assuming V=L, there is a mad permutation family in Sym(N).