کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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6414552 | 1630491 | 2015 | 34 صفحه PDF | دانلود رایگان |
Let Ï:ÎâG be a homomorphism of groups. We consider factorizations ÎâfMâgG of Ï having certain universal properties. First we continue the investigation (see [4]) of the case where g is a universal normal map (our term for a crossed module). Then we introduce and investigate a seemingly new dual case, where f is a universal normal map. These two factorizations are natural generalizations of the usual normal closure and normalizer of a subgroup.Iteration of these universal factorizations yields certain towers associated with the map Ï; we prove stability results for these towers. In one of the cases we get a generalization of the stability of the automorphisms tower of a center-less group. The case where g is a universal normal map is closely related to hyper-central group extensions, Bousfield's localizations, and the relative Schur multiplier H2(G,Î)=H2(BGâªBÏCone(BÎ)).Although our constructions here have strong ties to topological constructions, we take here a group theoretical point of view.
Journal: Journal of Algebra - Volume 423, 1 February 2015, Pages 1010-1043