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Consider the set of all 4-regular connected vertex-transitive graphs. By compactness, for every integer $R \ge 0$, there is an integer $N_R$, so that for every 4-regular vertex-transitive graph of ...

Let $\mathfrak A_i$ be groups ($i = 1, 2$), written multiplicatively, and $s$ a non-negative integer (here, as usual, I am abusing notation and denoting the operations of $\mathfrak A_1$ and $\...