Geodesic
A Class of Non-Central E-Functors
Canadian journal of mathematics, Tome 24 (1972) no. 1, pp. 1-4

Voir la notice de l'article provenant de la source Cambridge University Press

We refer the reader to [1, Chapters 1 and 2] for the notions of E-functor and centrality. Let R1 ⊆ R be the integral group rings of the groups G1 ⊆ G. Butler and Horrocks [1, Chapter 26] have shown that on the category of left, unitary R-modules the Hochschild E-functor determined by R1 is central. There are no examples of non-central Hochschild E-functors, and our purpose is to establish the existence of a class of such E-functors.Take G to be finite, non-abelian and let 5 be the centre of R. Denote by φ the Hochschild E-functor determined by S. We obtain a necessary condition for the centrality of φ in terms of the group structure of G. Let G* denote the subgroup of G generated by the commutators of G together with the set {gh (g): g £ G}, where h(g) is the class number of g in G. 
Chapman, G. R. A Class of Non-Central E-Functors. Canadian journal of mathematics, Tome 24 (1972) no. 1, pp. 1-4. doi: 10.4153/CJM-1972-001-7
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[1] 1. Butler, M. C. R. and Horrocks, G., Classes of extensions and resolutions, Philos. Trans. Roy. Soc. London Ser. A 254 (1961), 155–222. Google Scholar

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