Projective class group of crossed product

V. Muladze, G. Rakviashvili

Let R be a Dedekind ring, C0(R[π,ρ]) the projective class group of the crossed product R[π,ρ], M some class of subgroups of a finite group π, C0M(R[π,ρ]) the sum of the images of the maps C0(R[π',ρ]) → C0(R[π,ρ]) induced by i : π' ⊂ π, π' ∈ M. The main result of the paper is the study of some properties of the exponents of C0M(R[π',ρ]) in C(R[π,ρ]) for cyclic, elementary, and hyperelementary subgroups of π, under natural restrictions on R and π. 

Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 17(3) (2024), pp. 123-136