Minimal generating systems of a subgroup of SL(2, ℂ)

Abstract

Let H be any group. We call a cardinal number r the rank r(H) of H if H can be generated by a generating system X with cardinal number r but not by a generating system Y with cardinal number s less than r. Let r(H) be the rank of H.We call a generating system X of H a minimal generating system (M.G.S.) of H if X has the cardinal number r(H).In this note we prove the following.