We prove conjugate analogs of Mal’cev-Neumann-Taylor-Levi’s theorems. In other words, we characterize semigroups em- beddable in nilpotent groups of class n by means of conjugacy laws involving semigroup laws described by Mal’cev, Neumann and Taylor. Moreover we prove?that?a cancellative semigroup admitting conjugates is embeddable in a nilpotent group of?class 2 if and only if it satisfies the conjugacy law x^y^z = x^y. Also adapting Ore’s techniques we describe an exact procedure for embedding a cancellative semigroup admitting conjugates into a group.
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机译：我们证明了Mal’cev-Neumann-Taylor-Levi定理的共轭类似物。换句话说，我们通过涉及Malâcev，Neumann和Taylor描述的半群定律的共轭律来刻画可嵌入在n类幂等群中的半群。此外，我们证明了，当且仅当满足半共轭律x ^ y ^ z = x ^ y时，可加半群准共轭才可嵌入到2类幂等群中。我们还采用了Ore的技术，描述了将可准入半共轭缀合物嵌入到组中的确切程序。
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