The nilpotent multipliers of crossed modules
The article's objective consists in extending the notions of the \(c\)-nilpotent multiplier and of the \(c\)-stem cover of a group to the context of crossed modules, where \(c\) refers to the \(c\)-th (or \(c+1\)-st) term in the lower central series of a crossed module, and a \(c\)-stem cover is a sort of \(c\)-central extension. The main result of the paper is a five-term exact sequence in the \(c\)-nilpotent multiplier associated with an extension of crossed modules from which they deduce a generalization of a known theorem relating nilpotent crossed modules to their second homologies. They also prove that any \(c\)-stem extension of a perfect crossed module is a homomorphic image of its \(c\)-stem cover. They end with the proof that the \(c\)-nilpotent multipliers of a perfect crossed module are isomorphic to each other, extending a known result in group theory.
scientific article; zbMATH DE number 6817578