Local loop lemma
classification
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math.CO
keywords
loopalgebraicconnecteddigraphidempotentlocalstronglyassumptions
read the original abstract
We prove that an idempotent operation generates a loop from a strongly connected digraph containing directed cycles of all lengths under very mild (local) algebraic assumptions. Using the result, we reprove the existence of a weakest non-trivial idempotent equations, and that a strongly connected digraph with algebraic length 1 compatible with a Taylor term has a loop.
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