Extreme invariant means without minimal support
Lonnie Fairchild · Transactions of the American Mathematical Society · 1972
Let $S$ be a left amenable semigroup. We show that if $S$ has a subset satisfying a certain condition, then there is an extreme left invariant mean on $S$ whose support is not a minimal closed invariant subset of $\beta S$. Then we show that all infinite solvable groups and countably infinite locally finite groups have such subsets.