An group containing a neutral element is reducible. Thus, an group that is not reducible does not contain such elements. There exist groups with more than one neutral element. If the set of all neutral elements of an group is non-empty it forms an subgroup.Wiesław A. Dudek, Remarks to Głazek's results on n-ary groups, Discussiones Mathematicae. General Algebra and Applications 27 (2007), 199–233.
