Abstract

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

BibTeX

@article{MO-IJAC19,
   author = "Miroslav Olšák",
   title = "Loop conditions for strongly connected digraphs",
   journal = "International Journal of Algebra and Computation",
   editor  = "K. Kearnes",
   pages = "1--33",
   year = 2019,
   doi = 10.1142/S0218196720500083,
}