I'm working on the following qual question:
Suppose that $R$ is a finite ring with 1 such that every unit of $R$ has order dividing 24. Classify all such $R$.
My thoughts are I would like to try to show that there is an $x$ such that $axa = a$ for all $a$ in the ring. So maybe that can tell me the ring is von Neumann regular and then I can use that somehow. The other challenge is that we are only given information on the units, and we don't know much about the nonunits. Any guidance would be much appreciated