On permutable \(n\)-groups
An \(n\)-groupoid \((G,f)\) is called \(i\)-permutable iff \(f(x_ 1,...,x_{i- 1},f(x_ 1,...,x_ n),x_ i,...,x_{n-1})=x_ n\), for all \(x_ 1,x_ 2,...,x_ n\in G\) and fixed \(i\in\{1,2,...,n\}\). The authors prove that every such \(n\)-group is \(c\)-derived from a Boolean group. For \(i=n\) there exists an \(n\)-group which is \(n\)-permutable but it is not \(c\)-derived from any binary group. The class of \(n\)-permutable \(n\)-groups contains \(n\)-groups which are not derived from any \(k\)-group.
scientific article; zbMATH DE number 4110960