  In this expanded account of a talk given at the Oberwolfach
Arbeitsgemeinschaft "Totally Disconnected Groups", October 2014, we discuss
results of Nikolay Nikolov and Dan Segal on abstract quotients of compact
Hausdorff topological groups, paying special attention to the class of finitely
generated profinite groups. Our primary source is a paper, entitled "Generators
and commutators in finite groups; abstract quotients of compact groups", that
was published by Nikolov and Segal in 2012. Sidestepping all difficult and
technical proofs, we present a selection of accessible arguments to illuminate
key ideas in the subject.
