Some remarks on just-inpinitb groups

Let B(?) be the group of homeomcrphisms of the real line having bounded support. Higman has shown that (?) is simple. Schreier conjectured in 1928 that for any simple group, the outer automorphism groiftp is solvable. But it turns out that not only is Outer(?) non-sol table, but its derived series stabilizes after one step. Thus, although the counterexample is infinite, solvability fails as it must in finite groups (rather than because the derived series descends ad infinitum). For another (new) simple group G, Outer(G) is its own derived group. A countable counterexample is also given. Most important among the new simple groups is the group of diffeomorphisms (differentiable, but not necessarily C¹) of the real line having bounded support.