Noncrossed products of small exponent

Abstract:

Using the generic division algebras, we construct new division algebras and prove the following. Theorem. Let $m$, $n$ be positive integers, $m|n$, such that $m$ is divisible by every prime which divides $n$. If $k$ is any field, and there is a prime $p$ such that ${p^3}|m$, then there is a noncrossed product division $k$-algebra of exponent $m$ and degree $n$. If $k$ is a global field of characteristic 0, $p$ is an odd prime, and $k$ does not contain a primitive $p$th root of 1, we need only assume $p^2|m$.