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arXiv · 2408.12711

A proof for a part of noncrossed product theorem

Mehran Motiee
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Abstract

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 $p^3|n$.

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Mehran Motiee. 2024-08-22. A proof for a part of noncrossed product theorem. https://arxiv.org/abs/2408.12711

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