  Here, we show that the first isomorphism theorem, the orbit-stabilizer
theorem, and the non-uniqueness of solutions of underdetermined linear systems
are all manifestations of the same underlying algebraic property. We will call
this algebraic property kernel atomicity. It arises principally because
homomorphic maps induce partitions of their domain space into cosets, 'atoms'
whose cardinalities are equal to that of the kernel.
