Compact open subgroups in simple totally disconnected groups

It is shown that simplicity of a totally disconnected locally compact group G imposes (in the case when G is compactly generated) restrictions on the local structure of the group. For instance, if G is compactly generated and topologically simple, then no compact open subgroup of G is solvable. That G must be compactly generated for there to be a relationship between simplicity and local structure is demonstrated by several examples.