  For semisimple groups, possibly multiplied by U(1)'s, the number of
Yang-Mills gauge fields is equal to the number of generators of the group. In
this paper, it is shown that, for non-semisimple groups, the number of
Yang-Mills fields can be larger. These additional Yang-Mills fields are not
irrelevant because they appear in the gauge transformations of the original
Yang-Mills fields. Such non-semisimple Yang-Mills theories may lead to physical
consequences worth studying. The non-semisimple group with only two generators
that do not commute is studied in detail.
