2007/04/12 by Ivan D. Chipchakov, I. D. Chipchakov, Chipchakov, I. D.
Economics, Econometrics and Finance · Engineering · Mathematics · #Mathematical and Theoretical Analysis #Stability and Controllability of Differential Equations #Stochastic processes and financial applications #math.RA #msc:12E15 #msc:12F10 #msc:12J10 #msc:16K20
paper · pdf · doi:10.48550/arxiv.0704.1557
10 pages
arxiv created 2007/04/12 · arxiv updated 2009/12/01
Let E be a primarily quasilocal field, M/E a finite Galois extension and D a central division E-algebra of index divisible by [M\colon E]. In addition to the main result of Part I, this part of the paper shows that if the Galois group G(M/E) is not nilpotent, then M does not necessarily embed in D as an E-subalgebra. When E is quasilocal, we find the structure of the character group of its absolute Galois group; this enables us to prove that if E is strictly quasilocal and almost perfect, then the divisible part of the multiplicative group E ∗ equals the intersection of the norm groups of finite Galois extensions of E.