
Crossed modules provide a very useful tool in algebraic topology, algebraic K-theory, group cohomology and combinatorial group theory. They were introduced almost 40 years ago by J. H. C. Whitehead in his work on combinatorial homotopy theory. Given this illustrious start and their proven potential, it is strange that they are not very well known to the relevant sections of the mathematical fraternity. This article aims to introduce the general mathematical audience to this very elegant group theoretic structure. The article is well written, thorough and although assuming little or no acquaintance with algebraic topology, etc., it manages to get over the main points of the theory and use of crossed modules. It can be thoroughly recommended to anyone wishing to see what crossed modules are, why they are useful and how they arise. It is to be hoped that the limited circulation of the journal concerned will not inhibit the distribution of this article - perhaps an enlarged version might be published elsewhere.
Homological methods in group theory, Nonabelian homological algebra (category-theoretic aspects), group cohomology, Group rings, combinatorial group theory, Research exposition (monographs, survey articles) pertaining to algebraic topology, Group rings of infinite groups and their modules (group-theoretic aspects), crossed modules, homotopy theory, survey, Research exposition (monographs, survey articles) pertaining to group theory, Groupoids (i.e. small categories in which all morphisms are isomorphisms)
Homological methods in group theory, Nonabelian homological algebra (category-theoretic aspects), group cohomology, Group rings, combinatorial group theory, Research exposition (monographs, survey articles) pertaining to algebraic topology, Group rings of infinite groups and their modules (group-theoretic aspects), crossed modules, homotopy theory, survey, Research exposition (monographs, survey articles) pertaining to group theory, Groupoids (i.e. small categories in which all morphisms are isomorphisms)
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