In this paper we define the pullback cat^1-group and show that this Pullback has a right adjoint which is the induced cat^1-group. Later we show that this right adjoint is a pushout of category of cat^1-groups. We calculate the Peiffer subgroups to find a finite group of the source of induced cat^1-groups. The generating set of Peiffer subgroups are also given in this paper. All results are corrected by a GAP program package in . This paper also contains the some computational examples which are the calculation-induced cat^1-group and comparative times between the induced crossed modules and induced cat^1-groups.
ALP, MURAT (2001) "Induced Cat^1-groups," Turkish Journal of Mathematics: Vol. 25: No. 2, Article 1. Available at: https://journals.tubitak.gov.tr/math/vol25/iss2/1