  We construct ergodic discrete probability measure preserving equivalence
relations $\cR$ that has no proper ergodic normal subequivalence relations and
no proper ergodic finite-index subequivalence relations. We show that every
treeable equivalence relation satisfying a mild ergodicity condition and cost
$>1$ surjects onto every countable group with ergodic kernel. Lastly, we
provide a simple characterization of normality for subequivalence relations and
an algebraic description of the quotient.
