We prove that every strongly connected (not necessarily finite) digraph of algebraic length 1, which is compatible with an operation [Formula: see text] satisfying a non-trivial identity of the form [Formula: see text], has a loop.

中文翻译：

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强连通有向图的循环条件

我们证明了每个代数长度为 1 的强连通（不一定是有限）有向图，它与满足 [Formula: see text] 形式的非平凡身份的操作 [Formula: see text] 兼容，具有循环。