The nilpotent multipliers of crossed modules
type: Item
instance of: scholarly article
title: The nilpotent multipliers of crossed modules
zbMATH Open document ID: 1387.18024
author: Ali Reza Salemkar
author: Sajedeh Talebtash
author: Zahra Riyahi
published in: Journal of Pure and Applied Algebra
publication date: 2017-12-12T00:00:00Z
review text: 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.
reviewed by: Nadia Mazza
Mathematics Subject Classification ID: 18G05
Mathematics Subject Classification ID: 18G50
Mathematics Subject Classification ID: 20J99
zbMATH DE Number: 6817578
zbMATH Keywords: crossed modules
zbMATH Keywords: c-nilpotent multiplier
zbMATH Keywords: c-stem cover
zbMATH Keywords: c-stem extension
MaRDI profile type: Publication
full work available at URL: j.jpaa.2016.10.006
OpenAlex ID: W2547880300
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DOI: 10.1016/J.JPAA.2016.10.006
description: scientific article; zbMATH DE number 6817578