The paper's stated goal is to check that certain proposed ``subgroups'' are not actually subgroups at all. The proposed subgroups are groups that are direct products A × B. To show that A × B is not a subgroup, it suffices to show that A × 1 is not a subgroup, and that is the strategy taken in the paper and described by that sentence. They show that A is not isomorphic to a subgroup of SU(3), and so A × B is not isomorphic to a subgroup of SU(3).

I believe the statement they are making in symbols is: A ≤ A×B. In other words, they have stated the converse of the statement they use.

They also probably intend for B to be embedded in the center of SU(3), eliminating any worries about the direct product. Here they may also be using ⊗ to denote a mixture of the direct product and the Kronecker product. Even if A ∩ B ≠ 1, A ⊗ B = { ab : a in A, b in B } when B is central in SU(3).

It may be wise to avoid taking a sentence from a physics paper out of context and deriving logical consequences from it. This sentence is likely meant to explain a strategy, not state a mathematical truth. You should examine the sentence, but don't worry if you can derive contradictions from assuming the sentence is true (which would cause great worry in a math paper).