Let X be a nonempty set, and suppose that ? and ⊙ are binary operations on X such that, for all a, b, c e X, (a ? b) ⊙ c = a ? (b ⊙ c) and (a ⊙ b) ? c = a ⊙ (b ? c). Then we say that ? and ⊙ are compatible. In this article, we show that such operations arise on disjoint unions of isomorphic groups. In fact, given disjoint groups G and H, we show that G is isomorphic to H if and only if the group operations of G and H extend, respectively, to compatible group operations ?, ⊙ on G ∪ H.
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机译：令X为非空集，并假设？和⊙是对X的二进制运算，因此对于所有a，b，ce e，（a？b）⊙c = a？ （b c）和（a b）？ c ＝a⊙（b≥c）。那我们说呢？和⊙兼容。在本文中，我们证明了这种操作是在同构基团的不相交的并集上产生的。实际上，给定不相交的基团G和H，我们证明，当且仅当G和H的基团运算分别扩展到G∪H上的相容基团运算α，，时，G与H同构。
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