Step 1: Recall the defining feature:
A cyanobacterium is a prokaryote that photosynthesises, so it lacks a true nucleus.
Step 2: Eliminate the eukaryotes:
Spirogyra and Chlorella are both green algae with a nucleus, so both are eukaryotic and ruled out. Glomus is a fungus, also eukaryotic.
Final Answer:
Oscillatoria is the prokaryotic, filamentous blue-green alga, so it is the cyanobacterium.
$\boxed{\text{Oscillatoria}}$