Define a topological Lie group to be a group object in the category of topological manifolds. Until stated otherwise G is assumed finite-dimensional. Theorem 1.1. LetG be a compact, simple Hausdorff group. Then eitherG is a finite simple group or it is Lie. The latter are much easier to classify: they are U(n), O(n), U(n,H) mod their centers, or one of five special cases (of dimensions ≤ 248), ...

a normal subgroup $n$ of a group $g$ is said to be an‎ ‎$emph{omissible}$ subgroup of $g$ if it has the following property‎: ‎whenever $xleq g$ is such that $g=xn$‎, ‎then $g=x$‎. ‎in this note we construct various groups $g$‎, ‎each of which has an omissible subgroup $nneq 1$ such that $g/ncong sl_2(k)$ where $k$ is a field of positive characteristic‎.