ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

2. Algebra

1991 MS Classification: 16K Akbari, Saieed, Sharif University of Technology, Tehran, Iran On the group G(D) = \frac{D^{∗}}{RN_{D/F} (D^{∗})D′} Let D be a finite dimensional division ring with centre F and denote by D′ the derived group of D^{∗} = D − {0}. Suppose that RN_{D/F} : D → F is reduced norm function of D/F. In this paper we introduce a torsion abelian group G(D) = D^{∗}/RN_{D/F} (D^{∗})D′ related to D, where RN_{D/F} (D^{∗}) is the image of D^{∗} under RN_{D/F}, and show that if D_{1} and D_{2} are two finite dimensional division rings with centre F such that indices i(D_{1}) and i(D_{2}) are coprime, then we have G(D_{1} ⊗_{F} D_{2}) ≃ G(D_{1}) × G(D_{2}). Ultimately, we state some properties of this group.