Induced Cat1-groups

Authors : Murat Alp

Pages : 245-261

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Publication Date : 9999-12-31

Article Type : Makaleler

Abstract :In this paper we define the pullback cat1-group and show that this Pullback has a right adjoint which is the induced cat1-group. Later we show that this right adjoint is a pushout of category of cat1-groups. We calculate the Peiffer subgroups to find a finite group of the source of induced cat1-groups. The generating set of Peiffer subgroups are also given in this paper. All results are corrected by a GAP[13] program package in [4]. This paper also contains the some computational examples which are the calculation-induced cat1-group and comparative times between the induced crossed modules and induced cat1-groups.
Keywords : Pullback, Crossed module, Cat1-group, induced crossed modules, induced cat1-groups, Peiffer commutators, cocomplete, GAP.