Embedding problems with local conditions and the admissibility of finite groups

Let $k$ be a field of characteristic $p>0$, which has infinitely many discrete valuations. We show that every finite embedding problem for \Gal(k) with finitely many prescribed local conditions, whose kernel is a $p$-group, is properly solvable. We then apply this result in studying the admissibility of finite groups over global fields of positive characteristic. We also give another proof for a result of Sonn.Comment: 8 page

Triple Massey products over global fields

Let $K$ be a global field which contains a primitive $p$-th root of unity, where $p$ is a prime number. M. J. Hopkins and K. G. Wickelgren showed that for $p=2$, any triple Massey product over $K$ with respect to $\mathbb{F}_p$, contains 0 whenever it is defined. We show that this is true for all primes $p$.Comment: The final version of this paper appeared in Documenta Mathematica, Vol. 20 (2015) 1467-148

On p-embedding problems in characteristic p

Let K be a valued field of characteristic p>0 with non-p-divisible value group. We show that every finite embedding problem for K whose kernel is a p-group is properly solvable