2024/08/22 by Mehran Motiee, Motiee, Mehran
Mathematics · #Mathematics and Applications #Advanced Topology and Set Theory
paper · pdf · doi:10.48550/arxiv.2408.12711
The first examples of noncrossed product division algebras were given by Amitsur in 1972. His method is based on two basic steps: (1) If the universal division algebra U(k,n) is a G-crossed product then every division algebra of degree n over k should be a G-crossed product; (2) There are two division algebras over k whose maximal subfields do not have a common Galois group. In this note, we give a short proof for the second step in the case where \chr k\nmid n and p3|n.