2024/04/10 by H. V. Khanh, Huynh Viet Khanh, Nguyen Duc Anh Khoa +4
Mathematics · #Advanced Topics in Algebra #Finite Group Theory Research #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2404.06801
In this paper, we study the torsion subgroup, which is denoted by \rm TK1(E), of the Whitehead group E^*/[E^*,E^*] of a graded division algebra E which is finite dimensional over its center. In particular, we provide formulas for \rm TK1(E) in some special cases such as when E is unramified, totally ramified or semiramified. Using the formulas, we are able to compute the group \rm TK1(D) of a valued division ring D, which is finite dimensional over a henselian center.